Internal problem ID [14372]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number: 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 37
dsolve((t^2-y(t)^2)*diff(y(t),t)+(y(t)^2+t*y(t))=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= -t \\ y \left (t \right ) &= t -\sqrt {t^{2}-2 c_{1}} \\ y \left (t \right ) &= t +\sqrt {t^{2}-2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.515 (sec). Leaf size: 89
DSolve[(t^2-y[t]^2)*y'[t]+(y[t]^2+t*y[t])==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -t \\ y(t)\to t-\sqrt {t^2-e^{2 c_1}} \\ y(t)\to t+\sqrt {t^2-e^{2 c_1}} \\ y(t)\to -t \\ y(t)\to t-\sqrt {t^2} \\ y(t)\to \sqrt {t^2}+t \\ \end{align*}