Chapter 4.1, Problem 28P

To determine

To solve: The differential equation $t^2\left(t+3\right)y″\prime -3t\left(t+2\right)y″+6\left(1+t\right)y\prime -6y=0$ with initial condition $y_1\left(t\right)=t^2$, and $y_2\left(t\right)=t^3$.