54.2.321 problem 900

Internal problem ID [12195]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 900
Date solved : Wednesday, October 01, 2025 at 01:08:19 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

\begin{align*} y^{\prime }&=\frac {2 a \left (-y^{2}+4 a x -1\right )}{-y^{3}+4 y a x -y-2 a y^{6}+24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}} \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 48

ode:=diff(y(x),x) = 2*a*(-y(x)^2+4*a*x-1)/(-y(x)^3+4*a*x*y(x)-y(x)-2*a*y(x)^6+24*y(x)^4*a^2*x-96*y(x)^2*a^3*x^2+128*a^4*x^3); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {y}{2 a}+\frac {1}{32 a^{3} x -8 a^{2} y^{2}}-\frac {1}{16 a^{2} \left (-4 a x +y^{2}\right )^{2}}-c_1 = 0 \]

✓ Mathematica. Time used: 60.105 (sec). Leaf size: 381

ode=D[y[x],x] == (2*a*(-1 + 4*a*x - y[x]^2))/(128*a^4*x^3 - y[x] + 4*a*x*y[x] - 96*a^3*x^2*y[x]^2 - y[x]^3 + 24*a^2*x*y[x]^4 - 2*a*y[x]^6); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {Root}\left [8 \text {$\#$1}^5 a-16 \text {$\#$1}^4 a^2 c_1-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (-2+128 a^3 c_1 x\right )+128 \text {$\#$1} a^3 x^2-256 a^4 c_1 x^2+8 a x-1\&,1\right ]\\ y(x)&\to \text {Root}\left [8 \text {$\#$1}^5 a-16 \text {$\#$1}^4 a^2 c_1-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (-2+128 a^3 c_1 x\right )+128 \text {$\#$1} a^3 x^2-256 a^4 c_1 x^2+8 a x-1\&,2\right ]\\ y(x)&\to \text {Root}\left [8 \text {$\#$1}^5 a-16 \text {$\#$1}^4 a^2 c_1-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (-2+128 a^3 c_1 x\right )+128 \text {$\#$1} a^3 x^2-256 a^4 c_1 x^2+8 a x-1\&,3\right ]\\ y(x)&\to \text {Root}\left [8 \text {$\#$1}^5 a-16 \text {$\#$1}^4 a^2 c_1-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (-2+128 a^3 c_1 x\right )+128 \text {$\#$1} a^3 x^2-256 a^4 c_1 x^2+8 a x-1\&,4\right ]\\ y(x)&\to \text {Root}\left [8 \text {$\#$1}^5 a-16 \text {$\#$1}^4 a^2 c_1-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (-2+128 a^3 c_1 x\right )+128 \text {$\#$1} a^3 x^2-256 a^4 c_1 x^2+8 a x-1\&,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 - 1)/(128*a**4*x**3 - 96*a**3*x**2*y(x)**2 + 24*a**2*x*y(x)**4 + 4*a*x*y(x) - 2*a*y(x)**6 - y(x)**3 - y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out