4.43.36 \(y'''(x)-3 y''(x)+4 y'(x)-2 y(x)=e^x+\cos (x)\)

ODE
\[ y'''(x)-3 y''(x)+4 y'(x)-2 y(x)=e^x+\cos (x) \] ODE Classification

[[_3rd_order, _linear, _nonhomogeneous]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.118278 (sec), leaf count = 40

\[\left \{\left \{y(x)\to e^x \left (c_3+x\right )+\left (c_1 e^x+\frac {3}{10}\right ) \sin (x)+\left (c_2 e^x+\frac {1}{10}\right ) \cos (x)\right \}\right \}\]

Maple ✓
cpu = 0.065 (sec), leaf count = 34

\[ \left \{ y \left ( x \right ) ={\frac { \left ( 10\,\cos \left ( x \right ) {\it \_C2}+10\,{\it \_C3}\,\sin \left ( x \right ) +10\,x+10\,{\it \_C1} \right ) {{\rm e}^{x}}}{10}}+{\frac {\cos \left ( x \right ) }{10}}+{\frac {3\,\sin \left ( x \right ) }{10}} \right \} \] Mathematica raw input

DSolve[-2*y[x] + 4*y'[x] - 3*y''[x] + y'''[x] == E^x + Cos[x],y[x],x]

Mathematica raw output

{{y[x] -> E^x*(x + C[3]) + (1/10 + E^x*C[2])*Cos[x] + (3/10 + E^x*C[1])*Sin[x]}}

Maple raw input

dsolve(diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)+4*diff(y(x),x)-2*y(x) = exp(x)+cos(x), y(x),'implicit')

Maple raw output

y(x) = 1/10*(10*cos(x)*_C2+10*_C3*sin(x)+10*x+10*_C1)*exp(x)+1/10*cos(x)+3/10*si
n(x)