Internal problem ID [8211]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 631.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(y)]]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{2} \left (1+2 \sqrt {x^{3}-6 y}\right )}{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.273 (sec). Leaf size: 23
dsolve(diff(y(x),x) = 1/2*x^2*(1+2*(x^3-6*y(x))^(1/2)),y(x), singsol=all)
\[ c_{1}-x^{3}-\frac {1}{4}-\sqrt {x^{3}-6 y \relax (x )} = 0 \]
✓ Solution by Mathematica
Time used: 0.315 (sec). Leaf size: 31
DSolve[y'[x] == (x^2*(1 + 2*Sqrt[x^3 - 6*y[x]]))/2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^6}{6}+\left (\frac {1}{6}-2 c_1\right ) x^3-6 c_1{}^2 \\ \end{align*}