Internal problem ID [4526]
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]
\[ \boxed {y^{\prime } \sin \left (y\right )+\sin \left (x \right ) \cos \left (y\right )=\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 14
dsolve(diff(y(x),x)*sin(y(x))+sin(x)*cos(y(x))=sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \arccos \left ({\mathrm e}^{-\cos \left (x \right )} c_{1} +1\right ) \]
✓ Solution by Mathematica
Time used: 0.792 (sec). Leaf size: 81
DSolve[y'[x]*Sin[y[x]]+Sin[x]*Cos[y[x]]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 \text {Solve}\left [2 \cos (x) \tan \left (\frac {y(x)}{2}\right ) e^{\text {arctanh}(\cos (y(x)))}-\sqrt {\sin ^2(y(x))} \csc \left (\frac {y(x)}{2}\right ) \sec \left (\frac {y(x)}{2}\right ) \left (\log \left (\sec ^2\left (\frac {y(x)}{2}\right )\right )-2 \log \left (\tan \left (\frac {y(x)}{2}\right )\right )\right )=c_1,y(x)\right ] y(x)\to 0 \end{align*}