54.2.295 problem 874

Internal problem ID [12169]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 874
Date solved : Wednesday, October 01, 2025 at 01:05:38 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Abel]

\begin{align*} y^{\prime }&=\frac {\left (-256 a \,x^{2}+512+512 y^{2}+128 y a \,x^{4}+8 a^{2} x^{8}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 40

ode:=diff(y(x),x) = 1/512*(-256*x^2*a+512+512*y(x)^2+128*y(x)*a*x^4+8*a^2*x^8+512*y(x)^3+192*x^4*a*y(x)^2+24*y(x)*a^2*x^8+a^3*x^12)*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {a \,x^{4}}{8}-\frac {1}{3}+\frac {29 \operatorname {RootOf}\left (x^{2}-162 \int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} +6 c_1 \right )}{9} \]

✓ Mathematica. Time used: 0.119 (sec). Leaf size: 79

ode=D[y[x],x] == (x*(512 - 256*a*x^2 + 8*a^2*x^8 + a^3*x^12 + 128*a*x^4*y[x] + 24*a^2*x^8*y[x] + 512*y[x]^2 + 192*a*x^4*y[x]^2 + 512*y[x]^3))/512; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {\frac {1}{8} \left (3 a x^5+8 x\right )+3 x y(x)}{\sqrt [3]{29} \sqrt [3]{x^3}}}\frac {1}{K[1]^3-\frac {3 K[1]}{29^{2/3}}+1}dK[1]=\frac {1}{18} 29^{2/3} \left (x^3\right )^{2/3}+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-x*(a**3*x**12 + 24*a**2*x**8*y(x) + 8*a**2*x**8 + 192*a*x**4*y(x)**2 + 128*a*x**4*y(x) - 256*a*x**2 + 512*y(x)**3 + 512*y(x)**2 + 512)/512 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out