\[ 4 y^{(4)}(x)-12 y^{(3)}(x)+11 y''(x)-3 y'(x)-4 \cos (x)=0 \] ✓ Mathematica : cpu = 0.0739802 (sec), leaf count = 50
DSolve[-4*Cos[x] - 3*Derivative[1][y][x] + 11*Derivative[2][y][x] - 12*Derivative[3][y][x] + 4*Derivative[4][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {18 \sin (x)}{65}-\frac {14 \cos (x)}{65}+2 c_1 e^{x/2}+\frac {2}{3} c_2 e^{3 x/2}+c_3 e^x+c_4\right \}\right \}\] ✓ Maple : cpu = 0.07 (sec), leaf count = 32
dsolve(4*diff(diff(diff(diff(y(x),x),x),x),x)-12*diff(diff(diff(y(x),x),x),x)+11*diff(diff(y(x),x),x)-3*diff(y(x),x)-4*cos(x)=0,y(x))
\[y \left (x \right ) = 2 c_{2} {\mathrm e}^{\frac {x}{2}}+\frac {2 c_{3} {\mathrm e}^{\frac {3 x}{2}}}{3}+{\mathrm e}^{x} c_{1}+\frac {18 \sin \left (x \right )}{65}-\frac {14 \cos \left (x \right )}{65}+c_{4}\]