78.8.15 problem 15

Internal problem ID [18213]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 11:39:08 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _exact]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 14

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

\[ y = -x +\arccos \left (\frac {c_{1}}{x}\right ) \]

✓ Solution by Mathematica

Time used: 7.926 (sec). Leaf size: 35

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

\begin{align*} y(x)\to -x-\arccos \left (-\frac {c_1}{x}\right ) \\ y(x)\to -x+\arccos \left (-\frac {c_1}{x}\right ) \\ \end{align*}