Thread: verifying the solution of a differential equation

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

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

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

Originally Posted by Punch

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

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

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

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