63.5.7 problem 2(a)

Internal problem ID [13081]
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(a)
Date solved : Tuesday, January 28, 2025 at 04:51:41 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

dsolve(diff(x(t),t)=-(2/t)*x(t)+t,x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {t^{4}+4 c_{1}}{4 t^{2}} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 19

DSolve[D[x[t],t]==-(2/t)*x[t]+t,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {t^2}{4}+\frac {c_1}{t^2} \]