29.31.4 problem 903

Internal problem ID [5483]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 903
Date solved : Sunday, March 30, 2025 at 08:17:03 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

✓ Maple. Time used: 0.060 (sec). Leaf size: 36

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

\begin{align*} y &= \frac {-x^{2}-a}{x} \\ y &= \frac {c_{1}^{2}+4 c_{1} x -4 a}{4 x} \\ \end{align*}

✓ Mathematica. Time used: 1.309 (sec). Leaf size: 44

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

\begin{align*} y(x)\to \frac {-a+c_1 (-2 x+c_1)}{x} \\ y(x)\to -2 \sqrt {a} \\ y(x)\to 2 \sqrt {a} \\ \end{align*}

✗ Sympy

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

Timed Out