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 = 0.0198894 (sec), leaf count = 40
\[\left \{\left \{y(x)\to \frac {1}{4} e^{3 x} \left (4 c_1 e^x+4 c_2 e^{2 x}+2 x^2+6 x+7\right )\right \}\right \}\]
Maple ✓
cpu = 0.022 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={{\rm e}^{4\,x}}{\it \_C2}+{{\rm e}^{5\,x}}{\it \_C1}+{\frac { \left ( 2\,{x}^{2}+6\,x+7 \right ) {{\rm e}^{3\,x}}}{4}} \right \} \] 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),'implicit')
Maple raw output
y(x) = exp(4*x)*_C2+exp(5*x)*_C1+1/4*(2*x^2+6*x+7)*exp(3*x)