Show that the differential equation $\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{y}{x}-x$ may be reduced

Question

Show that the differential equation $\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{y}{x}-x$ may be reduced by the substitution $x=uy$ to the equation $\frac{1}{u^{2}}\frac{\mathrm{d}u}{\mathrm{d}x}=1$. Hence find $y$ in terms of $x$, given that $y=1$ and $x=1$.

Accepted Answer

$y=2x-x^2$

Solving by Substitution Q1

Solving by Substitution Q1

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Solution:

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