60.1.475 problem 488

Internal problem ID [10489]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 488
Date solved : Sunday, March 30, 2025 at 05:07:16 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

✓ Maple. Time used: 0.213 (sec). Leaf size: 72

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

\begin{align*} y &= -2 \sqrt {a x} \\ y &= 2 \sqrt {a x} \\ y &= \sqrt {-c_1^{2}+2 c_1 x +4 a x -x^{2}} \\ y &= -\sqrt {-x^{2}+\left (4 a +2 c_1 \right ) x -c_1^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.691 (sec). Leaf size: 85

ode=4*a^2 - 4*a*x + y[x]^2 - 4*a*y[x]*D[y[x],x] + y[x]^2*D[y[x],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