29.4.21 problem 110

Internal problem ID [4712]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 4
Problem number : 110
Date solved : Sunday, March 30, 2025 at 03:48:03 AM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

NotImplementedError : The given ODE f(x) + g(x)*sin(a*y(x)) + h(x)*cos(a*y(x)) + Derivative(y(x), x) cannot be solved by the lie group method