Internal problem ID [1710]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.10. Page 80
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-t \left (1+y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 14
dsolve(diff(y(t),t)=t*(1+y(t)),y(t), singsol=all)
\[ y \relax (t ) = -1+{\mathrm e}^{\frac {t^{2}}{2}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 24
DSolve[y'[t]==t*(1+y[t]),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -1+c_1 e^{\frac {t^2}{2}} \\ y(t)\to -1 \\ \end{align*}