60.7.42 problem 1639 (6.49)

Internal problem ID [11592]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1639 (6.49)
Date solved : Sunday, March 30, 2025 at 08:30:23 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

NotImplementedError : solving Abs(Derivative(y(x), x)) when the argument is not real or imaginary.