19.2.9 problem 9

Internal problem ID [3538]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.6, page 50
Problem number : 9
Date solved : Monday, January 27, 2025 at 07:41:05 AM
CAS classification : [_linear]

\begin{align*} x^{\prime } t +2 x&=4 \,{\mathrm e}^{t} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

dsolve(t*diff(x(t),t)+2*x(t)=4*exp(t),x(t), singsol=all)
 

\[ x = \frac {\left (4 t -4\right ) {\mathrm e}^{t}+c_{1}}{t^{2}} \]

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 20

DSolve[t*D[x[t],t]+2*x[t]==4*Exp[t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {4 e^t (t-1)+c_1}{t^2} \]