79.1.19 problem 4 (i)

Internal problem ID [18506]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 4 (i)
Date solved : Tuesday, January 28, 2025 at 11:51:22 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

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

\[ x = \frac {\left ({\mathrm e}^{3 t}+3 c_{1} \right ) {\mathrm e}^{-2 t}}{3} \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 21

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

\[ x(t)\to \frac {e^t}{3}+c_1 e^{-2 t} \]