78.1.8 problem 1.h

Internal problem ID [20934]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 1, First order ODEs. Problems section 1.5
Problem number : 1.h
Date solved : Thursday, October 02, 2025 at 06:49:32 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

\[ x = \left (\frac {t^{2}}{2}+c_1 \right ) {\mathrm e}^{2 t} \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 22

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

\begin{align*} x(t)&\to \frac {1}{2} e^{2 t} \left (t^2+2 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.095 (sec). Leaf size: 14

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

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