Internal problem ID [14363]
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: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y^{2}+t y-t y y^{\prime }=-t^{2}} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 22
dsolve(( t^2+t*y(t)+y(t)^2 )-( t*y(t) )*diff(y(t),t)=0,y(t), singsol=all)
\[ y \left (t \right ) = t \left (-\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-c_{1} -1}}{t}\right )-1\right ) \]
✓ Solution by Mathematica
Time used: 5.831 (sec). Leaf size: 31
DSolve[( t^2+t*y[t]+y[t]^2 )-( t*y[t] )*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -t \left (1+W\left (-\frac {e^{-1-c_1}}{t}\right )\right ) \\ y(t)\to -t \\ \end{align*}