Internal problem ID [1969]
Book: Ordinary Differential Equations, Robert H. Martin, 1983
Section: Problem 1.2-2, page 12
Problem number: 1.2-2 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {t y^{\prime }-y-t^{3}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 12
dsolve([t*diff(y(t),t)=y(t)+t^3,y(1) = -2],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (t^{2}-5\right ) t}{2} \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 24
DSolve[{y'[t]==y[t]+t^3,y[1]==-2},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -t (t (t+3)+6)+14 e^{t-1}-6 \\ \end{align*}