Internal problem ID [14413]
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: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y+\left (y+t \right ) y^{\prime }=t} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 51
dsolve((y(t)-t)+(t+y(t))*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {-c_{1} t -\sqrt {2 c_{1}^{2} t^{2}+1}}{c_{1}} \\ y \left (t \right ) &= \frac {-c_{1} t +\sqrt {2 c_{1}^{2} t^{2}+1}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.465 (sec). Leaf size: 94
DSolve[(y[t]-t)+(t+y[t])*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -t-\sqrt {2 t^2+e^{2 c_1}} \\ y(t)\to -t+\sqrt {2 t^2+e^{2 c_1}} \\ y(t)\to -\sqrt {2} \sqrt {t^2}-t \\ y(t)\to \sqrt {2} \sqrt {t^2}-t \\ \end{align*}