12.7.16 problem 16

Internal problem ID [1726]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page 91
Problem number : 16
Date solved : Monday, January 27, 2025 at 05:33:18 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.054 (sec). Leaf size: 16

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

\[ \ln \left (x \right )+\ln \left (y\right )-\ln \left (\sin \left (y\right )\right )+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.552 (sec). Leaf size: 27

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

\begin{align*} y(x)\to \text {InverseFunction}[\log (\sin (\text {$\#$1}))-\log (\text {$\#$1})\&][\log (x)+c_1] \\ y(x)\to 0 \\ \end{align*}