Internal problem ID [2058]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.6, page 50
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {t x^{\prime }+2 x-4 \,{\mathrm e}^{t}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 17
dsolve(t*diff(x(t),t)+2*x(t)=4*exp(t),x(t), singsol=all)
\[ x \relax (t ) = \frac {4 \left (t -1\right ) {\mathrm e}^{t}+c_{1}}{t^{2}} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 20
DSolve[t*x'[t]+2*x[t]==4*Exp[t],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {4 e^t (t-1)+c_1}{t^2} \\ \end{align*}