ODE
\[ (x+\sin (x)) y'''(x)+3 (\cos (x)+1) y''(x)-3 \sin (x) y'(x)-y(x) \cos (x)+\sin (x)=0 \] ODE Classification
[[_3rd_order, _fully, _exact, _linear]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.0795421 (sec), leaf count = 0 , could not solve
DSolve[Sin[x] - Cos[x]*y[x] - 3*Sin[x]*Derivative[1][y][x] + 3*(1 + Cos[x])*Derivative[2][y][x] + (x + Sin[x])*Derivative[3][y][x] == 0, y[x], x]
Maple ✓
cpu = 0.066 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C3}+{x}^{2}{\it \_C1}+x{\it \_C2}-\cos \left ( x \right ) }{x+\sin \left ( x \right ) }} \right \} \] Mathematica raw input
DSolve[Sin[x] - Cos[x]*y[x] - 3*Sin[x]*y'[x] + 3*(1 + Cos[x])*y''[x] + (x + Sin[x])*y'''[x] == 0,y[x],x]
Mathematica raw output
DSolve[Sin[x] - Cos[x]*y[x] - 3*Sin[x]*Derivative[1][y][x] + 3*(1 + Cos[x])*Derivative[2][y][x] + (x + Sin[x])*Derivative[3][y][x] == 0, y[x], x]
Maple raw input
dsolve((x+sin(x))*diff(diff(diff(y(x),x),x),x)+3*(1+cos(x))*diff(diff(y(x),x),x)-3*diff(y(x),x)*sin(x)-y(x)*cos(x)+sin(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C3+x^2*_C1+x*_C2-cos(x))/(x+sin(x))