Internal problem ID [1972]
Book: Ordinary Differential Equations, Robert H. Martin, 1983
Section: Problem 1.2-2, page 12
Problem number: 1.2-2 (f).
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: 0.008 (sec). Leaf size: 14
dsolve([t*diff(y(t),t)=-y(t)+t^3,y(1) = 2],y(t), singsol=all)
\[ y \relax (t ) = \frac {t^{4}+7}{4 t} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 25
DSolve[{y'[t]==-y[t]+t^3,y[1]==2},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t ((t-3) t+6)+4 e^{1-t}-6 \\ \end{align*}