ODE
\[ y''''(x)=y(x)+e^x \cos (x) \] ODE Classification
[[_high_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.066143 (sec), leaf count = 38
\[\left \{\left \{y(x)\to c_1 e^x+c_3 e^{-x}+c_4 \sin (x)+\left (c_2-\frac {e^x}{5}\right ) \cos (x)\right \}\right \}\]
Maple ✓
cpu = 0.096 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) ={\it \_C4}\,{{\rm e}^{-x}}+{\frac { \left ( 5\,{\it \_C1}-{{\rm e}^{x}} \right ) \cos \left ( x \right ) }{5}}+{\it \_C2}\,{{\rm e}^{x}}+{\it \_C3}\,\sin \left ( x \right ) \right \} \] Mathematica raw input
DSolve[y''''[x] == E^x*Cos[x] + y[x],y[x],x]
Mathematica raw output
{{y[x] -> E^x*C[1] + C[3]/E^x + (-E^x/5 + C[2])*Cos[x] + C[4]*Sin[x]}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x) = y(x)+exp(x)*cos(x), y(x),'implicit')
Maple raw output
y(x) = _C4*exp(-x)+1/5*(5*_C1-exp(x))*cos(x)+_C2*exp(x)+_C3*sin(x)