ODE
\[ y''(x)-3 y'(x)-4 y(x)=10 \cos (2 x) \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.213521 (sec), leaf count = 38
\[\left \{\left \{y(x)\to -\frac {3}{5} \sin (2 x)-\frac {4}{5} \cos (2 x)+c_1 e^{-x}+c_2 e^{4 x}\right \}\right \}\]
Maple ✓
cpu = 0.135 (sec), leaf count = 29
\[\left [y \left (x \right ) = {\mathrm e}^{-x} \textit {\_C2} +{\mathrm e}^{4 x} \textit {\_C1} -\frac {4 \cos \left (2 x \right )}{5}-\frac {3 \sin \left (2 x \right )}{5}\right ]\] Mathematica raw input
DSolve[-4*y[x] - 3*y'[x] + y''[x] == 10*Cos[2*x],y[x],x]
Mathematica raw output
{{y[x] -> C[1]/E^x + E^(4*x)*C[2] - (4*Cos[2*x])/5 - (3*Sin[2*x])/5}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-3*diff(y(x),x)-4*y(x) = 10*cos(2*x), y(x))
Maple raw output
[y(x) = exp(-x)*_C2+exp(4*x)*_C1-4/5*cos(2*x)-3/5*sin(2*x)]