Internal problem ID [2359]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 39, page 179
Problem number: 28.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {y-y^{\prime } x +{y^{\prime }}^{\frac {2}{3}}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 25
dsolve(y(x)=diff(y(x),x)*x-diff(y(x),x)^(2/3),y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {4}{27 x^{2}} y \left (x \right ) = 0 y \left (x \right ) = c_{1} x -c_{1}^{\frac {2}{3}} \end{align*}
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 23
DSolve[y[x]==y'[x]*x-y'[x]^(2/3),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x-c_1{}^{2/3} y(x)\to 0 \end{align*}