63.5.4 problem 1(d)

Internal problem ID [13078]
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 : Tuesday, January 28, 2025 at 04:51:35 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 33

DSolve[7*t^2*D[x[t],t]==3*x[t]-2*t,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{7} e^{\left .-\frac {3}{7}\right /t} \left (2 \operatorname {ExpIntegralEi}\left (\frac {3}{7 t}\right )+7 c_1\right ) \]