ODE
\[ y'''(x)-2 y''(x)-3 y'(x)=3 x^2+e^{-x} \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0807453 (sec), leaf count = 51
\[\left \{\left \{y(x)\to \frac {1}{144} \left (9 e^{-x} \left (-16 c_1+4 x+5\right )+48 c_2 e^{3 x}-16 x \left (3 x^2-6 x+14\right )\right )+c_3\right \}\right \}\]
Maple ✓
cpu = 0.036 (sec), leaf count = 40
\[ \left \{ y \left ( x \right ) ={\frac { \left ( 36\,x-144\,{\it \_C2}+45 \right ) {{\rm e}^{-x}}}{144}}-{\frac {{x}^{3}}{3}}+{\frac {2\,{x}^{2}}{3}}+{\frac {{{\rm e}^{3\,x}}{\it \_C1}}{3}}-{\frac {14\,x}{9}}+{\it \_C3} \right \} \] Mathematica raw input
DSolve[-3*y'[x] - 2*y''[x] + y'''[x] == E^(-x) + 3*x^2,y[x],x]
Mathematica raw output
{{y[x] -> (-16*x*(14 - 6*x + 3*x^2) + (9*(5 + 4*x - 16*C[1]))/E^x + 48*E^(3*x)*C[2])/144 + C[3]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)-3*diff(y(x),x) = 3*x^2+exp(-x), y(x),'implicit')
Maple raw output
y(x) = 1/144*(36*x-144*_C2+45)*exp(-x)-1/3*x^3+2/3*x^2+1/3*exp(3*x)*_C1-14/9*x+_C3