ODE
\[ y''(x)-2 y'(x)+y(x)=50 \cos (x) \cosh (x) \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0312428 (sec), leaf count = 41
\[\left \{\left \{y(x)\to e^{-x} \left (e^{2 x} \left (c_2 x+c_1\right )-4 \sin (x)+\left (3-25 e^{2 x}\right ) \cos (x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.084 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) = \left ( 3\,\cos \left ( x \right ) -4\,\sin \left ( x \right ) \right ) {{\rm e}^{-x}}+{{\rm e}^{x}} \left ( {\it \_C1}\,x+{\it \_C2}-25\,\cos \left ( x \right ) \right ) \right \} \] Mathematica raw input
DSolve[y[x] - 2*y'[x] + y''[x] == 50*Cos[x]*Cosh[x],y[x],x]
Mathematica raw output
{{y[x] -> (E^(2*x)*(C[1] + x*C[2]) + (3 - 25*E^(2*x))*Cos[x] - 4*Sin[x])/E^x}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-2*diff(y(x),x)+y(x) = 50*cos(x)*cosh(x), y(x),'implicit')
Maple raw output
y(x) = (3*cos(x)-4*sin(x))*exp(-x)+exp(x)*(_C1*x+_C2-25*cos(x))