\[ y^{(3)}(x) \sin (x)+(2 \cos (x)+1) y''(x)-\sin (x) y'(x)-\cos (x)=0 \] ✓ Mathematica : cpu = 0.842109 (sec), leaf count = 72
DSolve[-Cos[x] - Sin[x]*Derivative[1][y][x] + (1 + 2*Cos[x])*Derivative[2][y][x] + Sin[x]*Derivative[3][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {\sin \left (\frac {x}{2}\right ) \left (-2 \cos \left (\frac {x}{2}\right ) \sin ^{-1}(\cos (x))+\sqrt {2} \left (c_2 x \sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right ) (c_2 \log (2 (\cos (x)+1))+2 c_1)\right )\right )}{\cos (x)-1}+c_3\right \}\right \}\] ✓ Maple : cpu = 0.219 (sec), leaf count = 71
dsolve(diff(diff(diff(y(x),x),x),x)*sin(x)+(2*cos(x)+1)*diff(diff(y(x),x),x)-sin(x)*diff(y(x),x)-cos(x)=0,y(x))
\[y \left (x \right ) = \frac {\left (\sin ^{2}\left (x \right )\right ) \ln \left (\frac {-\cos \left (x \right )+1}{\sin \left (x \right )}\right ) c_{1}-\left (\sin ^{2}\left (x \right )\right ) \ln \left (\sin \left (x \right )\right ) c_{1}+\left (\sin ^{2}\left (x \right )\right ) c_{3}+\left (\cos \left (x \right )-1\right ) \left (c_{1} x +c_{2}+1\right ) \sin \left (x \right )-\left (\cos ^{2}\left (x \right )\right ) x +x}{\sin \left (x \right ) \left (\cos \left (x \right )-1\right )}\]