54.7.12 problem 1602 (6.12)

Internal problem ID [12861]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1602 (6.12)
Date solved : Wednesday, October 01, 2025 at 02:22:43 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} y^{\prime \prime }+6 a^{10} y^{11}-y&=0 \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 61

ode:=diff(diff(y(x),x),x)+6*a^10*y(x)^11-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \int _{}^{y}\frac {1}{\sqrt {-a^{10} \textit {\_a}^{12}+\textit {\_a}^{2}+c_1}}d \textit {\_a} -x -c_2 &= 0 \\ -\int _{}^{y}\frac {1}{\sqrt {-a^{10} \textit {\_a}^{12}+\textit {\_a}^{2}+c_1}}d \textit {\_a} -x -c_2 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 10.138 (sec). Leaf size: 49

ode=-y[x] + a^(2*5)*(1 + 5)*y[x]^(1 + 2*5) + D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\frac {1}{\sqrt {c_1+2 \left (\frac {K[1]^2}{2}-\frac {1}{2} a^{10} K[1]^{12}\right )}}dK[1]{}^2=(x+c_2){}^2,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(6*a**10*y(x)**11 - y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out