Consider the following initial value problem

$\frac{2y}{t^{2}1}-2t-(2-ln(t^{2}1))y^{\text{'}}=0$

$y(5)=0$

$($a$)$ What is the general solution to this ODE? You may use any method we have learned thus far. $($Hint: perhaps rearrange the terms so that it is in a form we are more familiar with$).(2$ points$)$

$($b$)$ Find the particular solution. $(1$ point$)$

$($c$)$ With the given initial condition, is there a unique solution? If so$,$ in what interval? Justify using the theorems in class. $(2$ points$)$