ODE
\[ y''''(x)-2 y''(x)+y(x)=\cos (x) \] ODE Classification
[[_high_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.264971 (sec), leaf count = 42
\[\left \{\left \{y(x)\to \frac {\cos (x)}{4}+e^{-x} \left (c_2 x+c_3 e^{2 x}+c_4 e^{2 x} x+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.179 (sec), leaf count = 31
\[\left [y \left (x \right ) = \frac {\cos \left (x \right )}{4}+\textit {\_C1} \,{\mathrm e}^{x}+\textit {\_C2} \,{\mathrm e}^{-x}+\textit {\_C3} x \,{\mathrm e}^{x}+\textit {\_C4} x \,{\mathrm e}^{-x}\right ]\] Mathematica raw input
DSolve[y[x] - 2*y''[x] + y''''[x] == Cos[x],y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + x*C[2] + E^(2*x)*C[3] + E^(2*x)*x*C[4])/E^x + Cos[x]/4}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)-2*diff(diff(y(x),x),x)+y(x) = cos(x), y(x))
Maple raw output
[y(x) = 1/4*cos(x)+_C1*exp(x)+_C2*exp(-x)+_C3*x*exp(x)+_C4*x*exp(-x)]