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`]]
\[ \boxed {y^{\prime }+y={\mathrm e}^{t} t} \]
✓ 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)
\[ y \left (t \right ) = \left (\frac {\left (2 t -1\right ) {\mathrm e}^{2 t}}{4}+c_{1} \right ) {\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 26
DSolve[y[t]+y'[t] == Exp[t]*t,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} e^t (2 t-1)+c_1 e^{-t} \]