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Differential Equations Separable Examples Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Use separation of variables to find the general solution to the given differential equation. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Use separation of variables to find the general solution to the given differential equation. First, write the derivative in fraction form. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Use separation of variables to find the general solution to the given differential equation. First, write the derivative in fraction form. Next do some algebra until all the y terms are on one side and t terms are on the other: typically you want to leave constants on the t side Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Use separation of variables to find the general solution to the given differential equation. First, write the derivative in fraction form. Next do some algebra until all the y terms are on one side and t terms are on the other: typically you want to leave constants on the t side Now we can integrate both sides and solve for y. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Use separation of variables to find the general solution to the given differential equation. First, write the derivative in fraction form. Next do some algebra until all the y terms are on one side and t terms are on the other: typically you want to leave constants on the t side Now we can integrate both sides and solve for y. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Use separation of variables to find the general solution to the given differential equation. First, write the derivative in fraction form. Next do some algebra until all the y terms are on one side and t terms are on the other: typically you want to leave constants on the t side Now we can integrate both sides and solve for y. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Use separation of variables to find the general solution to the given differential equation. First, write the derivative in fraction form. Next do some algebra until all the y terms are on one side and t terms are on the other: typically you want to leave constants on the t side Now we can integrate both sides and solve for y. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Use separation of variables to find the general solution to the given differential equation. First, write the derivative in fraction form. Next do some algebra until all the y terms are on one side and t terms are on the other: typically you want to leave constants on the t side Now we can integrate both sides and solve for y. This C is really e C. Since it is still an arbitrary constant we can just call it C. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Use separation of variables to find the general solution to the given differential equation. First, write the derivative in fraction form. Next do some algebra until all the y terms are on one side and t terms are on the other: typically you want to leave constants on the t side Now we can integrate both sides and solve for y. This C is really e C. Since it is still an arbitrary constant we can just call it C. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Use separation of variables to find the general solution to the given differential equation. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Use separation of variables to find the general solution to the given differential equation. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Use separation of variables to find the general solution to the given differential equation. We’ll need to use a substitution for the y integral: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Use separation of variables to find the general solution to the given differential equation. We’ll need to use a substitution for the y integral: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Use separation of variables to find the general solution to the given differential equation. We’ll need to use a substitution for the y integral: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Use separation of variables to find the general solution to the given differential equation. We’ll need to use a substitution for the y integral: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Use separation of variables to find the general solution to the given differential equation. We’ll need to use a substitution for the y integral: C is an arbitrary constant, so we can multiply by -2 and still call it C Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Use separation of variables to find the general solution to the given differential equation. We’ll need to use a substitution for the y integral: C is an arbitrary constant, so we can multiply by -2 and still call it C Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Use separation of variables to find the general solution to the given differential equation. We’ll need to use a substitution for the y integral: C is an arbitrary constant, so we can multiply by -2 and still call it C Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. First we separate and integrate Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. First we separate and integrate Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. First we separate and integrate Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB We need a substitution for this integral

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Find a particular solution to the given initial value problem. First we separate and integrate Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB We need a substitution for this integral

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Find a particular solution to the given initial value problem. First we separate and integrate Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB We need a substitution for this integral

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Find a particular solution to the given initial value problem. First we separate and integrate Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB We need a substitution for this integral

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Find a particular solution to the given initial value problem. First we separate and integrate Now we can find the constant from the initial value: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB We need a substitution for this integral

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Find a particular solution to the given initial value problem. First we separate and integrate Now we can find the constant from the initial value: Plugging this into our general solution we get Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB We need a substitution for this integral

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Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Find C from the initial value Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Find C from the initial value Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Don’t forget the +/- Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Don’t forget the +/- Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Don’t forget the +/- Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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