89.5.4 problem 4

Internal problem ID [24354]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 43
Problem number : 4
Date solved : Thursday, October 02, 2025 at 10:21:39 PM
CAS classification : [_linear]

\begin{align*} x^{\prime } t&=6 \,{\mathrm e}^{2 t} t +x \left (2 t -1\right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=t*diff(x(t),t) = 6*exp(2*t)*t+x(t)*(2*t-1); 
dsolve(ode,x(t), singsol=all);
 

\[ x = \frac {\left (3 t^{2}+c_1 \right ) {\mathrm e}^{2 t}}{t} \]

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

ode=t*D[x[t],t]== 6*t*Exp[2*t] + x[t] * (2*t-1); 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {e^{2 t} \left (3 t^2+c_1\right )}{t} \end{align*}

✓ Sympy. Time used: 0.189 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-6*t*exp(2*t) + t*Derivative(x(t), t) - (2*t - 1)*x(t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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