ODE
\[ y''''(x)-2 y''(x)+y(x)=\cos (x) \] ODE Classification
[[_high_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0979871 (sec), leaf count = 42
\[\left \{\left \{y(x)\to e^{-x} \left (c_2 x+c_3 e^{2 x}+c_4 e^{2 x} x+c_1\right )+\frac {\cos (x)}{4}\right \}\right \}\]
Maple ✓
cpu = 0.028 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) ={\frac {\cos \left ( x \right ) }{4}}+{\it \_C1}\,{{\rm e}^{x}}+{\it \_C2}\,{{\rm e}^{-x}}+{\it \_C3}\,x{{\rm e}^{x}}+{\it \_C4}\,x{{\rm e}^{-x}} \right \} \] 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),'implicit')
Maple raw output
y(x) = 1/4*cos(x)+_C1*exp(x)+_C2*exp(-x)+_C3*x*exp(x)+_C4*x*exp(-x)