Internal problem ID [14370]
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: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y^{2}-\left (t y-4 t^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 17
dsolve(y(t)^2=(t*y(t)-4*t^2)*diff(y(t),t),y(t), singsol=all)
\[ y \left (t \right ) = -4 t \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-c_{1}}}{4 t}\right ) \]
✓ Solution by Mathematica
Time used: 3.085 (sec). Leaf size: 29
DSolve[y[t]^2==(t*y[t]-4*t^2)*y'[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -4 t W\left (-\frac {e^{-\frac {c_1}{4}}}{4 t}\right ) \\ y(t)\to 0 \\ \end{align*}