ODE
\[ y''(x)+y(x)=e^{2 x} \cos (x) \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.185376 (sec), leaf count = 36
\[\left \{\left \{y(x)\to \frac {1}{8} \left (\left (e^{2 x}+8 c_1\right ) \cos (x)+\left (e^{2 x}+8 c_2\right ) \sin (x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.133 (sec), leaf count = 24
\[\left [y \left (x \right ) = \sin \left (x \right ) \textit {\_C2} +\textit {\_C1} \cos \left (x \right )+\frac {{\mathrm e}^{2 x} \left (\cos \left (x \right )+\sin \left (x \right )\right )}{8}\right ]\] Mathematica raw input
DSolve[y[x] + y''[x] == E^(2*x)*Cos[x],y[x],x]
Mathematica raw output
{{y[x] -> ((E^(2*x) + 8*C[1])*Cos[x] + (E^(2*x) + 8*C[2])*Sin[x])/8}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+y(x) = exp(2*x)*cos(x), y(x))
Maple raw output
[y(x) = sin(x)*_C2+_C1*cos(x)+1/8*exp(2*x)*(cos(x)+sin(x))]