Internal problem ID [8154]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 574.
ODE order: 1.
ODE degree: -1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(y)]]]
Solve \begin {gather*} \boxed {f \left (x -\frac {3 \left (y^{\prime }\right )^{2}}{2}\right )+\left (y^{\prime }\right )^{3}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 67
dsolve(f(x-3/2*diff(y(x),x)^2)+diff(y(x),x)^3-y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = f \left (c_{1}\right )-\frac {2 \sqrt {6 x^{3}-18 x^{2} c_{1}+18 x c_{1}^{2}-6 c_{1}^{3}}}{9} \\ y \relax (x ) = f \left (c_{1}\right )+\frac {2 \sqrt {6 x^{3}-18 x^{2} c_{1}+18 x c_{1}^{2}-6 c_{1}^{3}}}{9} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.299 (sec). Leaf size: 62
DSolve[f[x - (3*y'[x]^2)/2] - y[x] + y'[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{9} \left (9 f(c_1)+2 \sqrt {6} (x-c_1){}^{3/2}\right ) \\ y(x)\to \frac {1}{9} \left (9 f(c_1)-2 \sqrt {6} (x-c_1){}^{3/2}\right ) \\ \end{align*}