Question:

Let $y=y(x)$ be the solution of $\dfrac{dy}{dx}+\dfrac{5}{x(x^5+1)}y=\dfrac{(x^5+1)^2}{x^7}$, $x>0$, with $y(1)=2$. Then $y(2)$ is equal to

$\dfrac{637}{128}$

$\dfrac{679}{128}$

$\dfrac{693}{128}$

$\dfrac{697}{128}$

Step-by-Step Solution

Key Concept: IF $=\exp\!\int\frac{5}{x(x^5+1)}dx=\frac{x^5}{x^5+1}$. Multiply through and integrate.

$y(2)=\frac{693}{128}$.

Correct Answer: 3