Internal problem ID [8250]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 670.
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 \left (i-2 \sqrt {-x^{2}+4 \ln \relax (a )+4 \ln \relax (y)}\right ) y}{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 70
dsolve(diff(y(x),x) = 1/2*I*x*(I-2*(-x^2+4*ln(a)+4*ln(y(x)))^(1/2))*y(x),y(x), singsol=all)
\[ -\frac {\sqrt {-x^{2}+4 \ln \relax (a )+4 \ln \left (y \relax (x )\right )}}{2}+\frac {\arctan \left (\sqrt {-x^{2}+4 \ln \relax (a )+4 \ln \left (y \relax (x )\right )}\right )}{2}-\frac {i \ln \left (x^{2}-4 \ln \relax (a )-4 \ln \left (y \relax (x )\right )-1\right )}{4}-\frac {i x^{2}}{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 60.367 (sec). Leaf size: 59
DSolve[y'[x] == (I/2)*x*(I - 2*Sqrt[-x^2 + 4*Log[a] + 4*Log[y[x]]])*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\exp \left (\frac {1}{4} \left (-\text {ProductLog}\left (i e^{-x^2-1-4 c_1}\right )+x-1\right ) \left (\text {ProductLog}\left (i e^{-x^2-1-4 c_1}\right )+x+1\right )\right )}{a} \\ \end{align*}