57.5.4 problem 1(d)

Internal problem ID [14359]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.4.1. Integrating factors. Exercises page 41
Problem number : 1(d)
Date solved : Thursday, October 02, 2025 at 09:32:28 AM
CAS classification : [_linear]

\begin{align*} 7 t^{2} x^{\prime }&=3 x-2 t \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 22

ode:=7*t^2*diff(x(t),t) = 3*x(t)-2*t; 
dsolve(ode,x(t), singsol=all);
 

\[ x = \left (-\frac {2 \,\operatorname {Ei}_{1}\left (-\frac {3}{7 t}\right )}{7}+c_1 \right ) {\mathrm e}^{-\frac {3}{7 t}} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 33

ode=7*t^2*D[x[t],t]==3*x[t]-2*t; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {1}{7} e^{\left .-\frac {3}{7}\right /t} \left (2 \operatorname {ExpIntegralEi}\left (\frac {3}{7 t}\right )+7 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.954 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(7*t**2*Derivative(x(t), t) + 2*t - 3*x(t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \left (C_{1} + \frac {2 \operatorname {Ei}{\left (\frac {3}{7 t} \right )}}{7}\right ) e^{- \frac {3}{7 t}} \]