Question

verify that each given function is a solution of the

differential equation.

7.ty′\:−\:y\:=\:t^2;\:y\:=\:3t\:+\:t^2

Answer 1

Let us verify that the function $y(t)=3t+t^2$ is a solution of the differential equation $ty'-y=t^2$. taking into account that $y'(t)=3+2t$ and $ty'(t)-y(t)=t(3+2t)-(3t+t^2)=3t+2t^2-3t-t^2=t^2,$ we conclude that the function $y(t)=3t+t^2$ is a solution of the differential equation $ty'-y=t^2$.