20.3.10 problem Problem 10

Internal problem ID [3619]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 10
Date solved : Monday, January 27, 2025 at 07:47:41 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: 0.046 (sec). Leaf size: 20

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

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