32.6.5 problem Exercise 12.5, page 103

Internal problem ID [5870]
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
Date solved : Monday, January 27, 2025 at 01:21:51 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.360 (sec). Leaf size: 14

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

\[ y \left (x \right ) = \arccos \left (c_{1} {\mathrm e}^{-\cos \left (x \right )}+1\right ) \]

✓ Solution by Mathematica

Time used: 0.734 (sec). Leaf size: 81

DSolve[D[y[x],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*}