Internal problem ID [9005]
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)]`]]
\[ \boxed {y^{\prime }-\frac {i x \left (i-2 \sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y\right )}\right ) y}{2}=0} \]
✓ 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)
\[ \frac {\sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y \left (x \right )\right )}}{2}-\frac {\arctan \left (\sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y \left (x \right )\right )}\right )}{2}+\frac {i \ln \left (x^{2}-4 \ln \left (a \right )-4 \ln \left (y \left (x \right )\right )-1\right )}{4}+\frac {i x^{2}}{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 9.83 (sec). Leaf size: 86
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 \exp \left (\frac {1}{4} \left (-4 \log (a)-W\left (i e^{-x^2-1-4 c_1}\right ){}^2-2 W\left (i e^{-x^2-1-4 c_1}\right )+x^2-1\right )\right ) y(x)\to 0 y(x)\to \frac {e^{\frac {1}{4} \left (x^2-1\right )}}{a} \end{align*}