54.2.87 problem 663

Internal problem ID [11961]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 663
Date solved : Sunday, October 12, 2025 at 02:06:11 AM
CAS classification : [`y=_G(x,y')`]

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 27

ode:=diff(y(x),x) = (2*a+x^2*(-y(x)^2+4*a*x)^(1/2))/y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ -\sqrt {-y^{2}+4 a x}-\frac {x^{3}}{3}-c_1 = 0 \]

✓ Mathematica. Time used: 4.329 (sec). Leaf size: 161

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

\begin{align*} y(x)&\to -\frac {\sqrt {4096 a^6 x \left (36 a-x^5\right )+128 a^3 e^{c_1} x^3-e^{2 c_1}}}{192 a^3}\\ y(x)&\to \frac {\sqrt {4096 a^6 x \left (36 a-x^5\right )+128 a^3 e^{c_1} x^3-e^{2 c_1}}}{192 a^3}\\ y(x)&\to -\frac {\sqrt {a^6 x \left (36 a-x^5\right )}}{3 a^3}\\ y(x)&\to \frac {\sqrt {a^6 x \left (36 a-x^5\right )}}{3 a^3} \end{align*}

✗ Sympy

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

Timed Out