Internal problem ID [696]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, section 3.6, Variation of Parameters. page
190
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }-t \left (2+t \right ) y^{\prime }+\left (2+t \right ) y-2 t^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 18
dsolve(t^2*diff(y(t),t$2)-t*(t+2)*diff(y(t),t)+(t+2)*y(t) = 2*t^3,y(t), singsol=all)
\[ y \relax (t ) = c_{2} t +t \,{\mathrm e}^{t} c_{1}-2 t^{2} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 20
DSolve[t^2*y''[t]-t*(t+2)*y'[t]+(t+2)*y[t] == 2*t^3,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t \left (-2 t+c_2 e^t-2+c_1\right ) \\ \end{align*}