29.33.31 problem 994

Internal problem ID [5570]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 33
Problem number : 994
Date solved : Tuesday, March 04, 2025 at 10:21:59 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x^{2}-4 y^{2}\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-4 x^{2}+y^{2}&=0 \end{align*}

✓ Maple. Time used: 11.499 (sec). Leaf size: 93

ode:=(x^2-4*y(x)^2)*diff(y(x),x)^2+6*x*y(x)*diff(y(x),x)-4*x^2+y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y \left (x \right ) &= \frac {x \left (-\operatorname {RootOf}\left (\textit {\_Z}^{16}+2 \textit {\_Z}^{4} c_{1} x^{4}-c_{1} x^{4}\right )^{4}+1\right )}{\operatorname {RootOf}\left (\textit {\_Z}^{16}+2 \textit {\_Z}^{4} c_{1} x^{4}-c_{1} x^{4}\right )^{4}} \\ y \left (x \right ) &= \frac {\frac {\operatorname {RootOf}\left (\textit {\_Z}^{16}-2 \textit {\_Z}^{4} c_{1} x^{4}-c_{1} x^{4}\right )^{12}}{c_{1}}-x^{4}}{x^{3}} \\ \end{align*}

✓ Mathematica. Time used: 60.107 (sec). Leaf size: 3017

ode=(x^2-4 y[x]^2) (D[y[x],x])^2 +6 x y[x] D[y[x],x]-4 x^2+y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x**2 + 6*x*y(x)*Derivative(y(x), x) + (x**2 - 4*y(x)**2)*Derivative(y(x), x)**2 + y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out