Internal problem ID [14430]
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: 28.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {y-y^{\prime } t +2 {y^{\prime }}^{3}=0} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 35
dsolve(y(t)-t*diff(y(t),t)=-2*diff(y(t),t)^3,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= -\frac {\sqrt {6}\, t^{\frac {3}{2}}}{9} \\ y \left (t \right ) &= \frac {\sqrt {6}\, t^{\frac {3}{2}}}{9} \\ y \left (t \right ) &= c_{1} \left (-2 c_{1}^{2}+t \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 56
DSolve[y[t]-t*y'[t]==-2*y'[t]^3,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_1 \left (t-2 c_1{}^2\right ) \\ y(t)\to -\frac {1}{3} \sqrt {\frac {2}{3}} t^{3/2} \\ y(t)\to \frac {1}{3} \sqrt {\frac {2}{3}} t^{3/2} \\ \end{align*}