Internal problem ID [8205]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 625.
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 {i x^{2} \left (i-2 \sqrt {-x^{3}+6 y}\right )}{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 55
dsolve(diff(y(x),x) = 1/2*I*x^2*(I-2*(-x^3+6*y(x))^(1/2)),y(x), singsol=all)
\[ 2 i x^{3}+i \ln \left (x^{3}-6 y \relax (x )-1\right )-2 \arctan \left (\sqrt {-x^{3}+6 y \relax (x )}\right )+2 \sqrt {-x^{3}+6 y \relax (x )}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 60.198 (sec). Leaf size: 54
DSolve[y'[x] == (I/2)*x^2*(I - 2*Sqrt[-x^3 + 6*y[x]]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (-\text {ProductLog}\left (-i e^{-x^3-1-6 c_1}\right ) \left (2+\text {ProductLog}\left (-i e^{-x^3-1-6 c_1}\right )\right )+x^3-1\right ) \\ \end{align*}