ODE
\[ y''(x)-9 y'(x)+20 y(x)=e^{3 x} x^2 \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.175613 (sec), leaf count = 40
\[\left \{\left \{y(x)\to \frac {1}{4} e^{3 x} \left (2 x^2+6 x+4 c_1 e^x+4 c_2 e^{2 x}+7\right )\right \}\right \}\]
Maple ✓
cpu = 0.024 (sec), leaf count = 33
\[\left [y \left (x \right ) = {\mathrm e}^{4 x} \textit {\_C2} +{\mathrm e}^{5 x} \textit {\_C1} +\frac {\left (2 x^{2}+6 x +7\right ) {\mathrm e}^{3 x}}{4}\right ]\] Mathematica raw input
DSolve[20*y[x] - 9*y'[x] + y''[x] == E^(3*x)*x^2,y[x],x]
Mathematica raw output
{{y[x] -> (E^(3*x)*(7 + 6*x + 2*x^2 + 4*E^x*C[1] + 4*E^(2*x)*C[2]))/4}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-9*diff(y(x),x)+20*y(x) = x^2*exp(3*x), y(x))
Maple raw output
[y(x) = exp(4*x)*_C2+exp(5*x)*_C1+1/4*(2*x^2+6*x+7)*exp(3*x)]