63.5.10 problem 2(d)

Internal problem ID [13084]
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)
Date solved : Tuesday, January 28, 2025 at 04:51:47 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (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: 0.027 (sec). Leaf size: 19

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

\[ x(t)\to \frac {t^2}{3}+\frac {c_1}{t} \]