ODE
\[ y''(x)-2 y'(x)+y(x)=8 e^{3 x} x^2 \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0101736 (sec), leaf count = 32
\[\left \{\left \{y(x)\to e^x \left (c_2 x+c_1+e^{2 x} \left (2 x^2-4 x+3\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) = \left ( 2\,{x}^{2}-4\,x+3 \right ) {{\rm e}^{3\,x}}+{{\rm e}^{x}} \left ( {\it \_C1}\,x+{\it \_C2} \right ) \right \} \] Mathematica raw input
DSolve[y[x] - 2*y'[x] + y''[x] == 8*E^(3*x)*x^2,y[x],x]
Mathematica raw output
{{y[x] -> E^x*(E^(2*x)*(3 - 4*x + 2*x^2) + C[1] + x*C[2])}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-2*diff(y(x),x)+y(x) = 8*x^2*exp(3*x), y(x),'implicit')
Maple raw output
y(x) = (2*x^2-4*x+3)*exp(3*x)+exp(x)*(_C1*x+_C2)