Internal problem ID [8223]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 643.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)]]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x \left (-2+3 x \sqrt {x^{2}+3 y}\right )}{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.242 (sec). Leaf size: 22
dsolve(diff(y(x),x) = 1/3*x*(-2+3*x*(x^2+3*y(x))^(1/2)),y(x), singsol=all)
\[ c_{1}+\frac {x^{3}}{2}-\sqrt {x^{2}+3 y \relax (x )} = 0 \]
✓ Solution by Mathematica
Time used: 0.309 (sec). Leaf size: 31
DSolve[y'[x] == (x*(-2 + 3*x*Sqrt[x^2 + 3*y[x]]))/3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{12} \left (x^6-6 c_1 x^3-4 x^2+9 c_1{}^2\right ) \\ \end{align*}