60.2.336 problem 914

Internal problem ID [10910]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 914
Date solved : Sunday, March 30, 2025 at 07:22:27 PM
CAS classification : [_rational]

\begin{align*} y^{\prime }&=\frac {2 a \left (x y^{2}-4 a +x \right )}{-x^{3} y^{3}+4 a \,x^{2} y-x^{3} y+2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \end{align*}

✓ Maple. Time used: 0.057 (sec). Leaf size: 71

ode:=diff(y(x),x) = 2*a*(x*y(x)^2-4*a+x)/(-x^3*y(x)^3+4*a*x^2*y(x)-x^3*y(x)+2*a*y(x)^6*x^3-24*y(x)^4*a^2*x^2+96*y(x)^2*x*a^3-128*a^4); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {y^{4} x +\left (-4 a +x \right ) y^{2}-2 a}{2 y^{4} \left (-x y^{2}+4 a \right )^{2} a}+\frac {8 a y^{5}+2 y^{2}+1}{16 y^{4} a^{2}}+c_1 = 0 \]

✓ Mathematica. Time used: 60.773 (sec). Leaf size: 401

ode=D[y[x],x] == (2*a*(-4*a + x + x*y[x]^2))/(-128*a^4 + 4*a*x^2*y[x] - x^3*y[x] + 96*a^3*x*y[x]^2 - x^3*y[x]^3 - 24*a^2*x^2*y[x]^4 + 2*a*x^3*y[x]^6); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a x^2-8 \text {$\#$1}^4 a c_1 x^2-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (2 x^2+64 a^2 c_1 x\right )+128 \text {$\#$1} a^3-128 a^3 c_1-8 a x+x^2\&,1\right ] \\ y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a x^2-8 \text {$\#$1}^4 a c_1 x^2-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (2 x^2+64 a^2 c_1 x\right )+128 \text {$\#$1} a^3-128 a^3 c_1-8 a x+x^2\&,2\right ] \\ y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a x^2-8 \text {$\#$1}^4 a c_1 x^2-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (2 x^2+64 a^2 c_1 x\right )+128 \text {$\#$1} a^3-128 a^3 c_1-8 a x+x^2\&,3\right ] \\ y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a x^2-8 \text {$\#$1}^4 a c_1 x^2-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (2 x^2+64 a^2 c_1 x\right )+128 \text {$\#$1} a^3-128 a^3 c_1-8 a x+x^2\&,4\right ] \\ y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a x^2-8 \text {$\#$1}^4 a c_1 x^2-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (2 x^2+64 a^2 c_1 x\right )+128 \text {$\#$1} a^3-128 a^3 c_1-8 a x+x^2\&,5\right ] \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-2*a*(-4*a + x*y(x)**2 + x)/(-128*a**4 + 96*a**3*x*y(x)**2 - 24*a**2*x**2*y(x)**4 + 2*a*x**3*y(x)**6 + 4*a*x**2*y(x) - x**3*y(x)**3 - x**3*y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out