66.1.6 problem Problem 6

Internal problem ID [13782]
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 : Monday, March 31, 2025 at 08:11:41 AM
CAS classification : [[_linear, `class A`]]

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

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

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

\[ x = \frac {\left ({\mathrm e}^{5 t}+5 c_1 \right ) {\mathrm e}^{-3 t}}{5} \]

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

ode=D[x[t],t]+3*x[t]==Exp[2*t]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.135 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(3*x(t) - exp(2*t) + Derivative(x(t), t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{1} e^{- 3 t} + \frac {e^{2 t}}{5} \]