ODE
\[ y''''(x)=y(x)+\cos (x) \] ODE Classification
[[_high_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0412753 (sec), leaf count = 40
\[\left \{\left \{y(x)\to c_1 e^x+c_3 e^{-x}+\left (c_4-\frac {x}{4}\right ) \sin (x)+\left (c_2-\frac {1}{2}\right ) \cos (x)\right \}\right \}\]
Maple ✓
cpu = 0.063 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) ={\it \_C4}\,{{\rm e}^{-x}}+{\frac { \left ( 4\,{\it \_C1}-1 \right ) \cos \left ( x \right ) }{4}}+{\frac { \left ( -x+4\,{\it \_C3} \right ) \sin \left ( x \right ) }{4}}+{\it \_C2}\,{{\rm e}^{x}} \right \} \] Mathematica raw input
DSolve[y''''[x] == Cos[x] + y[x],y[x],x]
Mathematica raw output
{{y[x] -> E^x*C[1] + C[3]/E^x + (-1/2 + C[2])*Cos[x] + (-x/4 + C[4])*Sin[x]}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x) = y(x)+cos(x), y(x),'implicit')
Maple raw output
y(x) = _C4*exp(-x)+1/4*(4*_C1-1)*cos(x)+1/4*(-x+4*_C3)*sin(x)+_C2*exp(x)