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 = 0.266802 (sec), leaf count = 54
\[\left \{\left \{y(x)\to \frac {1}{9} \left (-3 x^3+6 x^2-14 x+\frac {9}{16} e^{-x} (4 x+5-16 c_1)+3 c_2 e^{3 x}+9 c_3\right )\right \}\right \}\]
Maple ✓
cpu = 0.226 (sec), leaf count = 46
\[\left [y \left (x \right ) = -{\mathrm e}^{-x} \textit {\_C1} +\frac {{\mathrm e}^{3 x} \textit {\_C2}}{3}+\frac {2 x^{2}}{3}-\frac {x^{3}}{3}+\frac {x \,{\mathrm e}^{-x}}{4}+\frac {5 \,{\mathrm e}^{-x}}{16}-\frac {14 x}{9}+\textit {\_C3}\right ]\] 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] -> (-14*x + 6*x^2 - 3*x^3 + (9*(5 + 4*x - 16*C[1]))/(16*E^x) + 3*E^(3*x)*C[2] + 9*C[3])/9}}
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))
Maple raw output
[y(x) = -exp(-x)*_C1+1/3*exp(3*x)*_C2+2/3*x^2-1/3*x^3+1/4*x*exp(-x)+5/16*exp(-x)-14/9*x+_C3]