ODE
\[ y''''(x)=y(x)+\cos (x) \] ODE Classification
[[_high_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.174888 (sec), leaf count = 40
\[\left \{\left \{y(x)\to c_1 e^x+c_3 e^{-x}+\left (-\frac {1}{2}+c_2\right ) \cos (x)+\left (-\frac {x}{4}+c_4\right ) \sin (x)\right \}\right \}\]
Maple ✓
cpu = 0.347 (sec), leaf count = 32
\[\left [y \left (x \right ) = -\frac {\cos \left (x \right )}{4}-\frac {x \sin \left (x \right )}{4}+\textit {\_C1} \cos \left (x \right )+\textit {\_C2} \,{\mathrm e}^{x}+\textit {\_C3} \sin \left (x \right )+\textit {\_C4} \,{\mathrm e}^{-x}\right ]\] 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] + (-1/4*x + C[4])*Sin[x]}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x) = y(x)+cos(x), y(x))
Maple raw output
[y(x) = -1/4*cos(x)-1/4*x*sin(x)+_C1*cos(x)+_C2*exp(x)+_C3*sin(x)+_C4*exp(-x)]