Internal problem ID [14391]
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: 51.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {y^{\prime } t -{y^{\prime }}^{3}-y=0} \]
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 35
dsolve(t*diff(y(t),t)-diff(y(t),t)^3=y(t),y(t), singsol=all)
\begin{align*} y \left (t \right ) &= -\frac {2 \sqrt {3}\, t^{\frac {3}{2}}}{9} \\ y \left (t \right ) &= \frac {2 \sqrt {3}\, t^{\frac {3}{2}}}{9} \\ y \left (t \right ) &= c_{1} \left (-c_{1}^{2}+t \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 52
DSolve[t*y'[t]-y'[t]^3==y[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_1 \left (t-c_1{}^2\right ) \\ y(t)\to -\frac {2 t^{3/2}}{3 \sqrt {3}} \\ y(t)\to \frac {2 t^{3/2}}{3 \sqrt {3}} \\ \end{align*}