Internal problem ID [1076]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y \sin \relax (y)+x \left (\sin \relax (y)-y \cos \relax (y)\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (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)
\[ \ln \relax (x )+\ln \left (y \relax (x )\right )-\ln \left (\sin \left (y \relax (x )\right )\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.586 (sec). Leaf size: 27
DSolve[(y[x]*Sin[y[x]])+(x*(Sin[y[x]]-y[x]*Cos[y[x]]))*y'[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*}