Internal problem ID [1646]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 6
Problem number: Example 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-2 y t -t=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve(diff(y(t),t)-2*t*y(t)=t,y(t), singsol=all)
\[ y \relax (t ) = -\frac {1}{2}+{\mathrm e}^{t^{2}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 24
DSolve[y'[t]-2*t*y[t]==t,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {1}{2}+c_1 e^{t^2} \\ y(t)\to -\frac {1}{2} \\ \end{align*}