ODE
\[ y'''(x)-\sin (x) y''(x)-2 \cos (x) y'(x)+y(x) \sin (x)=\log (x) \] ODE Classification
[[_3rd_order, _fully, _exact, _linear]]
Book solution method
TO DO
Mathematica ✓
cpu = 3.01148 (sec), leaf count = 57
\[\left \{\left \{y(x)\to e^{-\cos (x)} \left (\int _1^x\frac {1}{4} e^{\cos (K[1])} \left (2 \log (K[1]) K[1]^2-3 K[1]^2+4 c_1 K[1]+4 c_2\right )dK[1]+c_3\right )\right \}\right \}\]
Maple ✓
cpu = 0.379 (sec), leaf count = 36
\[\left [y \left (x \right ) = \left (\textit {\_C3} +\int \left (2 \textit {\_C1} x +\textit {\_C2} -\frac {3 x^{2}}{4}+\frac {x^{2} \ln \left (x \right )}{2}\right ) {\mathrm e}^{\cos \left (x \right )}d x \right ) {\mathrm e}^{-\cos \left (x \right )}\right ]\] Mathematica raw input
DSolve[Sin[x]*y[x] - 2*Cos[x]*y'[x] - Sin[x]*y''[x] + y'''[x] == Log[x],y[x],x]
Mathematica raw output
{{y[x] -> (C[3] + Inactive[Integrate][(E^Cos[K[1]]*(4*C[2] + 4*C[1]*K[1] - 3*K[1]^2 + 2*K[1]^2*Log[K[1]]))/4, {K[1], 1, x}])/E^Cos[x]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x)*sin(x)-2*diff(y(x),x)*cos(x)+y(x)*sin(x) = ln(x), y(x))
Maple raw output
[y(x) = (_C3+Int((2*_C1*x+_C2-3/4*x^2+1/2*x^2*ln(x))*exp(cos(x)),x))*exp(-cos(x))]