(Solved): Consider the initial value problem for the function y. y=ty2y2+4t2,y(1)=3,t1. (a) Transfor ...

Consider the initial value problem for the function $y$. $y^{\prime }=\frac{2y^2+4t^2}{ty},y(1)=3,t⩾1.$ (a) Transform the differential equation above for $y$ into a separable equation for $v(t)=\frac{y(t)}{t}$, You should get an equation $v^{\prime }=f(t,v)$. $v^{\prime }(t)=$ Note: In your answer type $v$ for $v(t)$, and $t$ for $t$ (b) Find an implicit expression of all solutions $y$ of the differental equation above, in the form $\psi (t,v)=c$, where $c$ collects all constant terms. (So, do not include any $c$ in your answer.) $\psi (t,v)$ Note: in your answer type $v$ for $v(t)$, and $t$ for $t$. (c) Find the explicit expression of the solution $y$ of the intial value problem above $y(t)=$