60.2.255 problem 831

Internal problem ID [10829]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 831
Date solved : Sunday, March 30, 2025 at 07:10:38 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\frac {2 a +\sqrt {-y^{2}+4 a x}+x^{2} \sqrt {-y^{2}+4 a x}+x^{3} \sqrt {-y^{2}+4 a x}}{y} \end{align*}

✓ Maple. Time used: 0.074 (sec). Leaf size: 35

ode:=diff(y(x),x) = (2*a+(-y(x)^2+4*a*x)^(1/2)+x^2*(-y(x)^2+4*a*x)^(1/2)+x^3*(-y(x)^2+4*a*x)^(1/2))/y(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 3.57 (sec). Leaf size: 79

ode=D[y[x],x] == (2*a + Sqrt[4*a*x - y[x]^2] + x^2*Sqrt[4*a*x - y[x]^2] + x^3*Sqrt[4*a*x - y[x]^2])/y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {1}{12} \sqrt {576 a x-\left (3 x^4+4 x^3+12 x+12 c_1\right ){}^2} \\ y(x)\to \frac {1}{12} \sqrt {576 a x-\left (3 x^4+4 x^3+12 x+12 c_1\right ){}^2} \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq((-2*a - x**3*sqrt(4*a*x - y(x)**2) - x**2*sqrt(4*a*x - y(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