63.5.36 problem 16-b(v)

Internal problem ID [13110]
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 : 16-b(v)
Date solved : Tuesday, January 28, 2025 at 04:53:02 AM
CAS classification : [_separable]

\begin{align*} x^{2}-t^{2} x^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

dsolve(x(t)^2-t^2*diff(x(t),t)=0,x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.123 (sec). Leaf size: 21

DSolve[x[t]^2-t^2*D[x[t],t]==0,x[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {t}{1-c_1 t} \\ x(t)\to 0 \\ \end{align*}