Internal problem ID [2616]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, End of chapter, page 61
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _exact]
Solve \begin {gather*} \boxed {\cos \left (x +y\right )-x \sin \left (x +y\right )-x \sin \left (x +y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \relax (x ) = -x +\arccos \left (\frac {c_{1}}{x}\right ) \]
✓ Solution by Mathematica
Time used: 8.505 (sec). Leaf size: 35
DSolve[Cos[x+y[x]]-x*Sin[x+y[x]]==x*Sin[x+y[x]]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x-\text {ArcCos}\left (-\frac {c_1}{x}\right ) \\ y(x)\to -x+\text {ArcCos}\left (-\frac {c_1}{x}\right ) \\ \end{align*}