54.7.29 problem 1619 (6.29)

Internal problem ID [12878]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1619 (6.29)
Date solved : Wednesday, October 01, 2025 at 02:43:53 AM
CAS classification : [NONE]

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

✗ Maple

ode:=diff(diff(y(x),x),x)+a*diff(y(x),x)+f(x)*sin(y(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=f[x]*Sin[y[x]] + a*D[y[x],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") 
a = symbols("a") 
y = Function("y") 
f = Function("f") 
ode = Eq(a*Derivative(y(x), x) + f(x)*sin(y(x)) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) + (f(x)*sin(y(x)) + Derivative(y(x), (x, 2)))/a cannot be solved by the factorable group method