Internal problem ID [14415]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Review exercises, page 80
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y^{2}+\left (t y+t^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.157 (sec). Leaf size: 45
dsolve(y(t)^2+(t*y(t)+t^2)*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {1+\sqrt {c_{1} t^{2}+1}}{c_{1} t} \\ y \left (t \right ) &= \frac {1-\sqrt {c_{1} t^{2}+1}}{c_{1} t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.71 (sec). Leaf size: 80
DSolve[y[t]^2+(t*y[t]+t^2)*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {e^{2 c_1}-\sqrt {e^{2 c_1} \left (t^2+e^{2 c_1}\right )}}{t} \\ y(t)\to \frac {\sqrt {e^{2 c_1} \left (t^2+e^{2 c_1}\right )}+e^{2 c_1}}{t} \\ y(t)\to 0 \\ \end{align*}