63.5.29 problem 15(d)

Internal problem ID [13103]
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 : 15(d)
Date solved : Tuesday, January 28, 2025 at 04:52:27 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

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

\[ y = \frac {3 t}{3 c_{1} t^{3}+1} \]

✓ Solution by Mathematica

Time used: 0.171 (sec). Leaf size: 24

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

\begin{align*} y(t)\to \frac {3 t}{1+3 c_1 t^3} \\ y(t)\to 0 \\ \end{align*}