Internal problem ID [8215]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 635.
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 (x +2 \sqrt {x^{3}-6 y}\right )}{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.36 (sec). Leaf size: 22
dsolve(diff(y(x),x) = 1/2*x*(x+2*(x^3-6*y(x))^(1/2)),y(x), singsol=all)
\[ c_{1}-\frac {3 x^{2}}{2}-\sqrt {x^{3}-6 y \relax (x )} = 0 \]
✓ Solution by Mathematica
Time used: 0.297 (sec). Leaf size: 33
DSolve[y'[x] == (x*(x + 2*Sqrt[x^3 - 6*y[x]]))/2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{24} \left (-9 x^4+4 x^3+36 c_1 x^2-36 c_1{}^2\right ) \\ \end{align*}