verifying the solution of a differential equation

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December 19th 2011, 09:36 PM
Punch

verifying the solution of a differential equation

verify that $y=cx^2+\frac{2}{x}$ is a general solution of the differential equation $x^2\frac{dy}{dx}-2xy+6=0$

$\frac{dy}{dx}=\frac{2xy-6}{x^2}$

How do I continue? y seems to be in the way
December 19th 2011, 10:18 PM
FernandoRevilla

Re: verifying the solution of a differential equation

Quote:

Originally Posted by Punch

verify that $y=cx^2+\frac{2}{x}$ is a general solution of the differential equation $x^2\frac{dy}{dx}-2xy+6=0$

$\frac{dy}{dx}=\frac{2xy-6}{x^2}$

How do I continue? y seems to be in the way

$y=cx^2+\frac{2}{x}\Rightarrow\frac{dy}{dx}=2cx-\frac{2}{x^2}$ , now substitute in the differential equation ...

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