ODE
\[ 4 y'''(x)-8 y''(x)-11 y'(x)-3 y(x)+18 e^x=0 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.183214 (sec), leaf count = 37
\[\left \{\left \{y(x)\to e^{-x/2} \left (e^{3 x/2}+c_2 x+c_3 e^{7 x/2}+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.026 (sec), leaf count = 26
\[\left [y \left (x \right ) = {\mathrm e}^{x}+\textit {\_C1} \,{\mathrm e}^{3 x}+\textit {\_C2} \,{\mathrm e}^{-\frac {x}{2}}+\textit {\_C3} \,{\mathrm e}^{-\frac {x}{2}} x\right ]\] Mathematica raw input
DSolve[18*E^x - 3*y[x] - 11*y'[x] - 8*y''[x] + 4*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (E^((3*x)/2) + C[1] + x*C[2] + E^((7*x)/2)*C[3])/E^(x/2)}}
Maple raw input
dsolve(4*diff(diff(diff(y(x),x),x),x)-8*diff(diff(y(x),x),x)-11*diff(y(x),x)-3*y(x)+18*exp(x) = 0, y(x))
Maple raw output
[y(x) = exp(x)+_C1*exp(3*x)+_C2*exp(-1/2*x)+_C3*exp(-1/2*x)*x]