Lesson 2a Separable Equations

# Lesson 2a Separable Equations - SeparableEquations...

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Separable Equations An ODE is Separable : when the equation can be written in the following form: f(y)y’=g(x). Examples: x yy 2 ' 3 y xy ' 2 y xy ' 2 x x x y y ' 2 xy y y y ' 2 x y y 1 ' 2

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Solving Separable ODEs Consider a separable ODE: . Now let and . Then we can consider the following: ) ( ' ) ( x g y y f dy y f y F ) ( ) ( dx x g x G ) ( ) ( dy ) ( ' ) ( x g y y f ) ( ) ( x g dx y f x x dy dx x g dx dx y f ) ( ) ( x y dx x g dy y f ) ( ) ( ur lution as it has no y’ anymore! c x G y F ) ( ) ( Our solution as it has no y anymore!
Strategy for Separable ODEs Step 1: get all of the y variables (including y’) on one side of the equation, and all of the x variables on the other side of the equation Step 2: Factor out y’. Remember that separable equations have f(y)y’. This means that if it is not multiplication with y’, it is not separable. Step 3: Integrate both sides (remember that dx cancels with to make dy). If you cannot integrate both sides, you may need to practice your integration dx dy techniques .

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Lesson 2a Separable Equations - SeparableEquations...

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