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 = 0.0164162 (sec), leaf count = 39
\[\left \{\left \{y(x)\to e^x \left (\left (c_3-\frac {1}{3}\right ) x+c_2+\frac {x^2}{2}+\frac {1}{9}\right )+c_1 e^{-2 x}\right \}\right \}\]
Maple ✓
cpu = 0.017 (sec), leaf count = 26
\[ \left \{ y \left ( x \right ) ={\it \_C2}\,{{\rm e}^{-2\,x}}+{\frac {{{\rm e}^{x}} \left ( 2\,{\it \_C3}\,x+{x}^{2}+2\,{\it \_C1} \right ) }{2}} \right \} \] 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),'implicit')
Maple raw output
y(x) = _C2*exp(-2*x)+1/2*exp(x)*(2*_C3*x+x^2+2*_C1)