19.2.9 problem 9

Internal problem ID [3538]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.6, page 50
Problem number : 9
Date solved : Sunday, March 30, 2025 at 01:46:38 AM
CAS classification : [_linear]

\begin{align*} t x^{\prime }+2 x&=4 \,{\mathrm e}^{t} \end{align*}

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

ode:=t*diff(x(t),t)+2*x(t) = 4*exp(t); 
dsolve(ode,x(t), singsol=all);
 

\[ x = \frac {\left (4 t -4\right ) {\mathrm e}^{t}+c_1}{t^{2}} \]

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 20

ode=t*D[x[t],t]+2*x[t]==4*Exp[t]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to \frac {4 e^t (t-1)+c_1}{t^2} \]

✓ Sympy. Time used: 0.228 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(t*Derivative(x(t), t) + 2*x(t) - 4*exp(t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \frac {\frac {C_{1}}{t} + 4 e^{t} - \frac {4 e^{t}}{t}}{t} \]