(a) Solve $x^{2} \frac{d^{2} y}{d x^{2}}-3 x \frac{d y}{d x}+4 y=x(\log x)^{2}$

Explanation

The given equation is a linear differential equation of second order. We have assumed $y=v x$ and substituted in the given equation to get a linear differential equation of second order in $v$. We have solved this equation to get the complementary function and particular integral. The general solution is obtained by adding the complementary function and particular integral.

(a) Solve $x^{2} \frac{d^{2} y}{d x^{2}}-3 x \frac{d y}{d x}+4 y=x(\log x)^{2}$

Explanation

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