Internal problem ID [11408]
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]
\[ \boxed {t x^{\prime }+x=t^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(t*diff(x(t),t)=-x(t)+t^2,x(t), singsol=all)
\[ x \left (t \right ) = \frac {t^{3}+3 c_{1}}{3 t} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 19
DSolve[t*x'[t]==-x[t]+t^2,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {t^2}{3}+\frac {c_1}{t} \]