60.1.425 problem 436

Internal problem ID [10439]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 436
Date solved : Sunday, March 30, 2025 at 04:43:23 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} \left (-x^{2}+1\right )-x^{4}&=0 \end{align*}

✓ Maple. Time used: 0.673 (sec). Leaf size: 56

ode:=x^2*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)+y(x)^2*(-x^2+1)-x^4 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -i x \\ y &= i x \\ y &= \frac {x \left (c_1^{2} {\mathrm e}^{-x}-{\mathrm e}^{x}\right )}{2 c_1} \\ y &= -\frac {x \left (-c_1^{2} {\mathrm e}^{x}+{\mathrm e}^{-x}\right )}{2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.149 (sec). Leaf size: 26

ode=-x^4 + (1 - x^2)*y[x]^2 - 2*x*y[x]*D[y[x],x] + x^2*D[y[x],x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -x \sinh (x-c_1) \\ y(x)\to x \sinh (x+c_1) \\ \end{align*}

✗ Sympy

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

Timed Out