75.1.11 problem 13

Internal problem ID [16674]
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 : Tuesday, January 28, 2025 at 08:25:52 PM
CAS classification : [`y=_G(x,y')`]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 5

dsolve([diff(y(x),x)=sin(x*y(x)),y(0) = 0],y(x), singsol=all)
 

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 6

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

\[ y(x)\to 0 \]