Internal problem ID [8258]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 678.
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^{2} \left (x +1+2 x \sqrt {x^{3}-6 y}\right )}{2 \left (x +1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.515 (sec). Leaf size: 37
dsolve(diff(y(x),x) = 1/2*x^2*(x+1+2*x*(x^3-6*y(x))^(1/2))/(x+1),y(x), singsol=all)
\[ c_{1}-x^{3}+\frac {3 x^{2}}{2}-3 x +3 \ln \left (x +1\right )-\frac {1}{2}-\sqrt {x^{3}-6 y \relax (x )} = 0 \]
✓ Solution by Mathematica
Time used: 3.633 (sec). Leaf size: 87
DSolve[y'[x] == (x^2*(1 + x + 2*x*Sqrt[x^3 - 6*y[x]]))/(2*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{24} \left (-x (x (x (x (4 (x-3) x+33)+4)-30)+132)+12 c_1 x (x (2 x-3)+6)+12 \log (x+1) (x (x (2 x-3)+6)-3 \log (x+1)+11-6 c_1)-121-36 c_1{}^2+132 c_1\right ) \\ \end{align*}