Internal problem ID [4018]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.5, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } \sin \relax (y)+\sin \relax (x ) \cos \relax (y)-\sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.117 (sec). Leaf size: 14
dsolve(diff(y(x),x)*sin(y(x))+sin(x)*cos(y(x))=sin(x),y(x), singsol=all)
\[ y \relax (x ) = \arccos \left ({\mathrm e}^{-\cos \relax (x )} c_{1}+1\right ) \]
✓ Solution by Mathematica
Time used: 7.345 (sec). Leaf size: 31
DSolve[y'[x]*Sin[y[x]]+Sin[x]*Cos[y[x]]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 \\ y(x)\to 2 \text {ArcSin}\left (e^{\frac {1}{4} (-2 \cos (x)+c_1)}\right ) \\ y(x)\to 0 \\ \end{align*}