67.1.3 problem Problem 1(c)

Internal problem ID [13879]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 2, First Order Equations. Problems page 149
Problem number : Problem 1(c)
Date solved : Monday, March 31, 2025 at 08:16:02 AM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

ode:=diff(y(x),x) = sin(x*y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]==Sin[x*y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sin(x*y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -sin(x*y(x)) + Derivative(y(x), x) cannot be solved by the lie group method