SeparableEquation

SeparableEquation - dx--=-2 3 2 1 2 9 THE SOLUTION...

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SEPARABLE EQUATION Solving a Separable first order differential equation See the document FirstOrderDiffEq.pdf for a comparison between this and other methods. THE PROBLEM 24. p66 9 2 2 3 2 2 x y x y y + ′ = / Find the general solution. The equation is separable is it can be written in the form ( ) ( ) terms of terms of y dy x dx = DETERMINE IF THIS IS A SEPARABLE EQUATION Rewrite the equation: x y x y dy dx 3 2 2 2 2 9 / = - Divide by y 2 : y x x dy dx - = - 2 3 2 2 1 9 / Divide by x 3 2 / : y x x dy dx - - = - 2 3 2 1 2 9 / / Multiply by dx . The equation is now in the form of a Separable Equation: ( ) ( ) / / y dy x x
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Unformatted text preview: dx--=-2 3 2 1 2 9 THE SOLUTION Integrate the equation: y dy x dx x dx y C x C x C---- =--+ = -+-+ 2 3 2 1 2 1 1 1 2 2 3 2 3 9 2 6 / / / / ( ) Consolidate the constants and multiply by -1: Factor out x-1/2 : y x x C y x x Cx--= + + = + + 1 1 2 3 2 1 2 2 1 2 2 6 1 1 2 6 / / / / ( ) THE ANSWER Invert the equation to get the answer: y x x x Cx ( ) / ( ) / / = + + 1 2 2 1 2 6 2 Tom Penick tomzap@eden.com www.teicontrols.com/notes 12/9/1997...
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