Internal problem ID [8152]
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: 0.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]
\[ \boxed {f \left (x -\frac {3 {y^{\prime }}^{2}}{2}\right )+{y^{\prime }}^{3}-y=0} \]
✓ Solution by Maple
Time used: 0.047 (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 \left (x \right ) = f \left (c_{1} \right )-\frac {2 \sqrt {-6 c_{1}^{3}+18 x \,c_{1}^{2}-18 x^{2} c_{1} +6 x^{3}}}{9} \\ y \left (x \right ) = f \left (c_{1} \right )+\frac {2 \sqrt {-6 c_{1}^{3}+18 x \,c_{1}^{2}-18 x^{2} c_{1} +6 x^{3}}}{9} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.389 (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*}