38.1.6 problem 6

Internal problem ID [6423]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Test excercise 24. page 1067
Problem number : 6
Date solved : Monday, January 27, 2025 at 02:01:14 PM
CAS classification : [_separable]

\begin{align*} x \cos \left (y\right ) y^{\prime }-\sin \left (y\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 8

dsolve(x*cos(y(x))*diff(y(x),x)-sin(y(x))=0,y(x), singsol=all)
 

\[ y = \arcsin \left (c_1 x \right ) \]

✓ Solution by Mathematica

Time used: 9.243 (sec). Leaf size: 17

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

\begin{align*} y(x)\to \arcsin \left (e^{c_1} x\right ) \\ y(x)\to 0 \\ \end{align*}