60.8.17 problem 1854

Internal problem ID [11778]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 7, non-linear third and higher order
Problem number : 1854
Date solved : Sunday, March 30, 2025 at 09:15:05 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} y^{\prime \prime }-f \left (y\right )&=0 \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 51

ode:=diff(diff(y(x),x),x)-f(y(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \int _{}^{y}\frac {1}{\sqrt {2 \int f \left (\textit {\_b} \right )d \textit {\_b} +c_1}}d \textit {\_b} -x -c_2 &= 0 \\ -\int _{}^{y}\frac {1}{\sqrt {2 \int f \left (\textit {\_b} \right )d \textit {\_b} +c_1}}d \textit {\_b} -x -c_2 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 40

ode=-f[y[x]]+ D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

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

Timed Out