76.4.21 problem 27

Internal problem ID [17415]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.6 (Exact equations and integrating factors). Problems at page 100
Problem number : 27
Date solved : Tuesday, January 28, 2025 at 10:06:27 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 9

dsolve(1/(x/y(x)-sin(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.126 (sec). Leaf size: 32

DSolve[1+(x/y[x]-Sin[y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=\frac {\int _1^{y(x)}K[1] \sin (K[1])dK[1]}{y(x)}+\frac {c_1}{y(x)},y(x)\right ] \]