Internal problem ID [2478]
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]
\[ \boxed {t y^{\prime }-y=t^{3}} \] With initial conditions \begin {align*} [y \left (1\right ) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve([t*diff(y(t),t)=y(t)+t^3,y(1) = -2],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (t^{2}-5\right ) t}{2} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 27
DSolve[{y'[t]==y[t]+t^3,y[1]==-2},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -t^3-3 t^2-6 t+14 e^{t-1}-6 \]