Internal problem ID [8226]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 646.
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^{3}+x^{2}+2 \sqrt {x^{3}-6 y}}{2 \left (x +1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.352 (sec). Leaf size: 23
dsolve(diff(y(x),x) = 1/2*(x^3+x^2+2*(x^3-6*y(x))^(1/2))/(x+1),y(x), singsol=all)
\[ c_{1}-3 \ln \left (x +1\right )-\sqrt {x^{3}-6 y \relax (x )} = 0 \]
✓ Solution by Mathematica
Time used: 0.458 (sec). Leaf size: 35
DSolve[y'[x] == (x^2/2 + x^3/2 + Sqrt[x^3 - 6*y[x]])/(1 + x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (x^3-9 \log ^2(x+1)+18 c_1 \log (x+1)-9 c_1{}^2\right ) \\ \end{align*}