ODE
\[ y'''(x)-3 y'(x)+2 y(x)=3 e^x \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.159836 (sec), leaf count = 39
\[\left \{\left \{y(x)\to e^x \left (\frac {x^2}{2}+\left (-\frac {1}{3}+c_3\right ) x+\frac {1}{9}+c_2\right )+c_1 e^{-2 x}\right \}\right \}\]
Maple ✓
cpu = 0.026 (sec), leaf count = 27
\[\left [y \left (x \right ) = \frac {x^{2} {\mathrm e}^{x}}{2}+\textit {\_C1} \,{\mathrm e}^{x}+\textit {\_C2} \,{\mathrm e}^{-2 x}+\textit {\_C3} \,{\mathrm e}^{x} x\right ]\] Mathematica raw input
DSolve[2*y[x] - 3*y'[x] + y'''[x] == 3*E^x,y[x],x]
Mathematica raw output
{{y[x] -> C[1]/E^(2*x) + E^x*(1/9 + x^2/2 + C[2] + x*(-1/3 + C[3]))}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-3*diff(y(x),x)+2*y(x) = 3*exp(x), y(x))
Maple raw output
[y(x) = 1/2*x^2*exp(x)+_C1*exp(x)+_C2*exp(-2*x)+_C3*exp(x)*x]