##### 4.45.10 $$(x+\sin (x)) y'''(x)+3 (\cos (x)+1) y''(x)-3 \sin (x) y'(x)-y(x) \cos (x)+\sin (x)=0$$

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 = 0.234413 (sec), leaf count = 28

$\left \{\left \{y(x)\to \frac {-\cos (x)+x (c_3 x+c_2)+c_1}{x+\sin (x)}\right \}\right \}$

Maple
cpu = 0.638 (sec), leaf count = 43

$\left [y \left (x \right ) = \frac {x^{2} \textit {\_C1}}{x +\sin \left (x \right )}+\frac {\textit {\_C2} x}{x +\sin \left (x \right )}-\frac {\cos \left (x \right )}{x +\sin \left (x \right )}+\frac {\textit {\_C3}}{x +\sin \left (x \right )}\right ]$ 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

{{y[x] -> (C[1] + x*(C[2] + x*C[3]) - Cos[x])/(x + Sin[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))

Maple raw output

[y(x) = x^2/(x+sin(x))*_C1+1/(x+sin(x))*_C2*x-cos(x)/(x+sin(x))+1/(x+sin(x))*_C3
]