Internal problem ID [14367]
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: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y+\left (y+t \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve((y(t))+(t+y(t))*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} 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: 0.735 (sec). Leaf size: 84
DSolve[y[t]+(t+y[t])*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} 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 0 \\ y(t)\to -\sqrt {t^2}-t \\ y(t)\to \sqrt {t^2}-t \\ \end{align*}