Show that the differential equation $\frac{\mathrm{d}y}{\mathrm{d}x}-\frac{2y}{x}={{x}^{3}}$ may be

Question

Show that the differential equation $\frac{\mathrm{d}y}{\mathrm{d}x}-\frac{2y}{x}={{x}^{3}}$ may be reduced by the substitution $y=u{{x}^{2}}$ to $\frac{\mathrm{d}u}{\mathrm{d}x}=x$. Hence find the general solution for $y$ in terms of $x$. [4]

Accepted Answer

$\displaystyle y=\frac12x^4+Cx^2$

2023 TMJC P1 Q10

2023 TMJC P1 Q10

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