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The differential equation $x \frac{d y}{d x}-y=x^2$, has the general solution |
$y-x^3=2 C x$ $y-x^2=Cx$ $2 y+x^2=2 C x$ $y+x^2=2 C x$ |
$y-x^2=Cx$ |
$\frac{xd y}{d x}-y=x^2$ so $\frac{xdy-ydx}{x^2}=dx$ so $\int d(\frac{y}{x})=\int dx$ so $\frac{y}{x}=x+C$ so $y=x^2+Cx$ so $y-x^2=Cx$ |
