29.33.12 problem 974

Internal problem ID [5551]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 33
Problem number : 974
Date solved : Tuesday, March 04, 2025 at 09:59:44 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 a x +y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.166 (sec). Leaf size: 72

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

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

✓ Mathematica. Time used: 0.689 (sec). Leaf size: 85

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

\begin{align*} y(x)\to -\frac {\sqrt {16 a^3 x-4 a^2 x^2-4 a c_1 x-c_1{}^2}}{2 a} \\ y(x)\to \frac {\sqrt {16 a^3 x-4 a^2 x^2-4 a c_1 x-c_1{}^2}}{2 a} \\ \end{align*}

✗ Sympy

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

Timed Out