Internal problem ID [15082]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 7, Total differential equations. The integrating factor. Exercises page
61
Problem number: 194.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {\cos \left (y\right ) y^{\prime }+\sin \left (y\right )=-\sin \left (x \right )-x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve(( x+sin(x)+sin(y(x)))+( cos(y(x)) )*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\arcsin \left (x +\frac {\sin \left (x \right )}{2}-\frac {\cos \left (x \right )}{2}-1+c_{1} {\mathrm e}^{-x}\right ) \]
✓ Solution by Mathematica
Time used: 33.179 (sec). Leaf size: 61
DSolve[( x+Sin[x]+Sin[y[x]])+( Cos[y[x]] )*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \arcsin \left (\frac {1}{2} \left (-2 x-\sin (x)+\cos (x)+2 c_1 e^{-x}+2\right )\right ) \\ y(x)\to -\arcsin \left (\frac {1}{2} \left (2 x+\sin (x)-\cos (x)-2 c_1 e^{-x}-2\right )\right ) \\ \end{align*}