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Published byDylan Ellis Modified over 6 years ago

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1Chapter 2

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Example 3Chapter 2

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EXAMPLE 5Chapter 2

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Solution 6Chapter 2

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9 Method for solving First Order Differential Equations Differential Equations Method for solving First Order Differential Equations Differential Equations

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Methods Variable Separable Reducible to variable separable Exact Differential Equation Integrating Factor

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Separable Variable x is independent variable and y is dependent variable or are separable forms of the differential equation or General solution can be solved by directly integrating both the sides + c Where c is constant of integration 11 Chapter 2 DO YOU REMEMBER INTEGRATION FORMULA? Variable Separable Differential Equation Chapter 2

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Separation of Variables Definition A differential equation of the type y’ = f(x)g(y) is separable. Example Separable differential equations can often be solved with direct integration. This may lead to an equation which defines the solution implicitly rather than directly. Variable Separable Differential Equation Chapter 2

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EXAMPLE: 13Chapter 2 Variable Separable Differential Equation Chapter 2

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EXAMPLE: 14Chapter 2 Variable Separable Differential Equation Chapter 2

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To find the particular solution, we apply the given initial condition, when x =1, y = 3 is solution of initial value problem 15Chapter 2 Variable Separable Differential Equation Chapter 2

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16Chapter 2 Variable Separable Differential Equation Chapter 2

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17Chapter 2 Variable Separable Differential Equation Chapter 2

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Chapter 218 Note1: If we have Integrating by parts Note.2. If we have Integrating by parts Note.3. If we have

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Chapter 219 Variable Separable Differential Equation Chapter 2

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Chapter 220

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Chapter 221

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