66.1.6 problem Problem 6

Internal problem ID [13853]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 6
Date solved : Tuesday, January 28, 2025 at 06:05:23 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} x^{\prime }+3 x&={\mathrm e}^{2 t} \end{align*}

✓ Solution by Maple

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

dsolve(diff(x(t),t)+3*x(t)=exp(2*t),x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {\left ({\mathrm e}^{5 t}+5 c_{1} \right ) {\mathrm e}^{-3 t}}{5} \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 23

DSolve[D[x[t],t]+3*x[t]==Exp[2*t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {e^{2 t}}{5}+c_1 e^{-3 t} \]