a) Verify that the function

$\displaystyle {y}={x}^{{2}}+{\frac{{{c}}}{{{x}^{{2}}}}}$

is a solution of the differential equation

$\displaystyle {x}{y}'+{2}{y}={4}{x}^{{2}},\ {\left({x}\gt{0}\right)}.$

b) Find the value of $\displaystyle {c}$ for which the solution satisfies the initial condition $\displaystyle {y}{\left({5}\right)}={1}$.

$\displaystyle {c}=$ Preview Question 6