69.1.11 problem 13

Internal problem ID [17961]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 1. Basic concepts and definitions. Exercises page 18
Problem number : 13
Date solved : Sunday, October 12, 2025 at 05:33:15 AM
CAS classification : [`y=_G(x,y')`]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 5

ode:=diff(y(x),x) = sin(x*y(x)); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 6

ode=D[y[x],x]==Sin[x*y[x]]; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 0 \end{align*}

✗ Sympy

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