60.1.78 problem 79

Internal problem ID [10092]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 79
Date solved : Sunday, March 30, 2025 at 03:15:22 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

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