Linear differential equation/y' is y over t/Inhomogeneous part is t^7/Exercise

a) Find all solutions for the ordinary differential equation (${}t\in \mathbb {R}$)

${}y'={\frac {y}{t}}\,.$

b) Find all solutions for the ordinary differential equation (${}t\in \mathbb {R}$)

${}y'={\frac {y}{t}}+t^{7}\,.$

c) Solve the initial value problem

$y'={\frac {y}{t}}+t^{7}{\text{ and }}y(1)=5.$

Create a solution