4.42.49 \(y'''(x)-2 y'(x)+4 y(x)=e^x \cos (x)\)

ODE
\[ y'''(x)-2 y'(x)+4 y(x)=e^x \cos (x) \] ODE Classification

[[_3rd_order, _linear, _nonhomogeneous]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.19856 (sec), leaf count = 53

\[\left \{\left \{y(x)\to c_3 e^{-2 x}-\frac {1}{100} e^x (5 x-2 (9+50 c_2)) \cos (x)+\frac {1}{100} e^x (15 x+1+100 c_1) \sin (x)\right \}\right \}\]

Maple ✓
cpu = 0.561 (sec), leaf count = 49

\[\left [y \left (x \right ) = \left (\frac {9 \,{\mathrm e}^{x}}{50}-\frac {x \,{\mathrm e}^{x}}{20}\right ) \cos \left (x \right )+\left (\frac {{\mathrm e}^{x}}{100}+\frac {3 x \,{\mathrm e}^{x}}{20}\right ) \sin \left (x \right )+{\mathrm e}^{-2 x} \textit {\_C1} +\textit {\_C2} \,{\mathrm e}^{x} \cos \left (x \right )+\textit {\_C3} \,{\mathrm e}^{x} \sin \left (x \right )\right ]\] Mathematica raw input

DSolve[4*y[x] - 2*y'[x] + y'''[x] == E^x*Cos[x],y[x],x]

Mathematica raw output

{{y[x] -> C[3]/E^(2*x) - (E^x*(5*x - 2*(9 + 50*C[2]))*Cos[x])/100 + (E^x*(1 + 15
*x + 100*C[1])*Sin[x])/100}}

Maple raw input

dsolve(diff(diff(diff(y(x),x),x),x)-2*diff(y(x),x)+4*y(x) = exp(x)*cos(x), y(x))

Maple raw output

[y(x) = (9/50*exp(x)-1/20*x*exp(x))*cos(x)+(1/100*exp(x)+3/20*x*exp(x))*sin(x)+e
xp(-2*x)*_C1+_C2*exp(x)*cos(x)+_C3*exp(x)*sin(x)]