60.2.94 problem 670

Internal problem ID [10668]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 670
Date solved : Sunday, March 30, 2025 at 06:18:17 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} y^{\prime }&=\frac {i x \left (i-2 \sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y\right )}\right ) y}{2} \end{align*}

✓ Maple. Time used: 0.037 (sec). Leaf size: 68

ode:=diff(y(x),x) = 1/2*I*x*(I-2*(-x^2+4*ln(a)+4*ln(y(x)))^(1/2))*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {i \ln \left (x^{2}-4 \ln \left (a \right )-4 \ln \left (y\right )-1\right )}{4}+\frac {\sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y\right )}}{2}-\frac {\arctan \left (\sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y\right )}\right )}{2}+\frac {i x^{2}}{2}-c_1 = 0 \]

✓ Mathematica. Time used: 3.83 (sec). Leaf size: 86

ode=D[y[x],x] == (I/2)*x*(I - 2*Sqrt[-x^2 + 4*Log[a] + 4*Log[y[x]]])*y[x]; 
ic={}; 
DSolve[{ode,ic},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*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(x*(-2*sqrt(-x**2 + 4*log(a) + 4*log(y(x))) + complex(0, 1))*complex(0, -1/2)*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out