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6.4 day 1 Separable Differential Equations Jefferson Memorial, Washington DC Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2007
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A separable differential equation can be expressed as the product of a function of x and a function of y. Example: Multiply both sides by dx and divide both sides by y 2 to separate the variables. (Assume y 2 is never zero.)
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Separable Differential Equations A separable differential equation can be expressed as the product of a function of x and a function of y. Example: Combined constants of integration
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Example: Separable differential equation Combined constants of integration
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Example: We now have y as an implicit function of x. We can find y as an explicit function of x by taking the tangent of both sides. Notice that we can not factor out the constant C, because the distributive property does not work with tangent.
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Use 2ND, = to get the prime symbol. To do the same problem on the TI-89: Enter the differential equation as shown: Use the multiplication symbol. Independent variable Dependent variable enter Press F3 Calc, C deSolve( to open the differential equation solver.
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(Use copy and paste to insert the expression) To do the same problem on the TI-89: In this case, the calculator does not explicitly solve for y, so we can try using the “solve” function. This solution includes restrictions on the domain. Highlight the solution and scroll right to see the rest of the answer. Press F3 Calc, C deSolve( to open the differential equation solver.
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