29.33.21 problem 983

Internal problem ID [5560]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 33
Problem number : 983
Date solved : Sunday, March 30, 2025 at 08:40:35 AM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out