54.7.18 problem 1608 (6.18)

Internal problem ID [12867]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1608 (6.18)
Date solved : Wednesday, October 01, 2025 at 02:23:44 AM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta \sin \left (x \right )&=0 \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)+a^2*sin(y(x))-beta*sin(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : solve: Cannot solve -BETA*sin(x) + a**2*sin(y(x)) + Derivative(y(x), (x, 2))