23.2.149 problem 152

Internal problem ID [5504]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 152
Date solved : Friday, October 03, 2025 at 01:29:47 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 0.782 (sec). Leaf size: 56

ode:=x^2*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)-x^4+(-x^2+1)*y(x)^2 = 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: 0.093 (sec). Leaf size: 26

ode=x^2 (D[y[x],x])^2-2 x y[x] D[y[x],x]-x^4+(1-x^2)y[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