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Question

Let $y=y(x)$ be the solution of the differential equation $\frac{d y}{d x}+\frac{5}{x\left(x^{5}+1\right)} y=\frac{\left(x^{5}+1\right)^{2}}{x^{7}}, x > 0$. If $y(1)=2$, then $y(2)$ is equal to :

$\frac{693}{128}$
$\frac{697}{128}$
$\frac{637}{128}$
$\frac{679}{128}$

Solution

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