Internal problem ID [10384]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {7 t^{2} x^{\prime }-3 x+2 t=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(7*t^2*diff(x(t),t)=3*x(t)-2*t,x(t), singsol=all)
\[ x \left (t \right ) = \left (-\frac {2 \,\operatorname {Ei}_{1}\left (-\frac {3}{7 t}\right )}{7}+c_{1} \right ) {\mathrm e}^{-\frac {3}{7 t}} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 33
DSolve[7*t^2*x'[t]==3*x[t]-2*t,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*}