60.7.18 problem 1608 (6.18)

Internal problem ID [11607]
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 : Monday, January 27, 2025 at 11:24:45 PM
CAS classification : [NONE]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved