54.2.341 problem 920

Internal problem ID [12215]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 920
Date solved : Wednesday, October 01, 2025 at 01:14:17 AM
CAS classification : [_rational]

\begin{align*} y^{\prime }&=\frac {2 y^{6} \left (1+4 x y^{2}+y^{2}\right )}{y^{3}+4 y^{5} x +y^{5}+2+24 x y^{2}+96 x^{2} y^{4}+128 x^{3} y^{6}} \end{align*}

✗ Maple

ode:=diff(y(x),x) = 2*y(x)^6*(1+4*x*y(x)^2+y(x)^2)/(y(x)^3+4*y(x)^5*x+y(x)^5+2+24*x*y(x)^2+96*y(x)^4*x^2+128*x^3*y(x)^6); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 11.045 (sec). Leaf size: 301

ode=D[y[x],x] == (2*y[x]^6*(1 + y[x]^2 + 4*x*y[x]^2))/(2 + 24*x*y[x]^2 + y[x]^3 + 96*x^2*y[x]^4 + y[x]^5 + 4*x*y[x]^5 + 128*x^3*y[x]^6); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-8*x*y(x)**2 - 2*y(x)**2 - 2)*y(x)**6/(128*x**3*y(x)**6 + 96*x**2*y(x)**4 + 4*x*y(x)**5 + 24*x*y(x)**2 + y(x)**5 + y(x)**3 + 2) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out