Internal problem ID [10390]
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: 2(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x^{\prime } t -t^{2}+x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(t*diff(x(t),t)=-x(t)+t^2,x(t), singsol=all)
\[ x \left (t \right ) = \frac {\frac {t^{3}}{3}+c_{1}}{t} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 19
DSolve[t*x'[t]==-x[t]+t^2,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {t^2}{3}+\frac {c_1}{t} \\ \end{align*}