Internal problem ID [1652]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 9
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y+y^{\prime }-t \,{\mathrm e}^{t}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(y(t)+diff(y(t),t) = exp(t)*t,y(t), singsol=all)
\[ y \relax (t ) = \left (\frac {\left (2 t -1\right ) {\mathrm e}^{2 t}}{4}+c_{1}\right ) {\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 26
DSolve[y[t]+y'[t] == Exp[t]*t,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{4} e^t (2 t-1)+c_1 e^{-t} \\ \end{align*}