Internal problem ID [12601]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.3 page 47
Problem number: 16 (vii).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-y t=t} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(t),t)=t+t*y(t),y(t), singsol=all)
\[ y \left (t \right ) = -1+{\mathrm e}^{\frac {t^{2}}{2}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 24
DSolve[y'[t]==t+t*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*}