Internal problem ID [6338]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 47.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {t y^{\prime \prime }+4 y^{\prime }-t^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(t*diff(y(t),t$2)+4*diff(y(t),t)=t^2,y(t), singsol=all)
\[ y \relax (t ) = \frac {t^{3}}{18}-\frac {c_{1}}{3 t^{3}}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 23
DSolve[t*y''[t]+4*y'[t]==t^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {t^6-6 c_1}{18 t^3}+c_2 \\ \end{align*}