ODE
\[ y'''(x)-6 y''(x)+12 y'(x)-8 y(x)=e^{2 x} x^2 \] ODE Classification
[[_3rd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0239945 (sec), leaf count = 34
\[\left \{\left \{y(x)\to \frac {1}{60} e^{2 x} \left (60 c_3 x^2+60 c_2 x+60 c_1+x^5\right )\right \}\right \}\]
Maple ✓
cpu = 0.017 (sec), leaf count = 36
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{5} \left ( {{\rm e}^{x}} \right ) ^{2}}{60}}+{{\rm e}^{2\,x}}{\it \_C1}+{\it \_C2}\,{x}^{2}{{\rm e}^{2\,x}}+{\it \_C3}\,{{\rm e}^{2\,x}}x \right \} \] Mathematica raw input
DSolve[-8*y[x] + 12*y'[x] - 6*y''[x] + y'''[x] == E^(2*x)*x^2,y[x],x]
Mathematica raw output
{{y[x] -> (E^(2*x)*(x^5 + 60*C[1] + 60*x*C[2] + 60*x^2*C[3]))/60}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-6*diff(diff(y(x),x),x)+12*diff(y(x),x)-8*y(x) = x^2*exp(2*x), y(x),'implicit')
Maple raw output
y(x) = 1/60*x^5*exp(x)^2+exp(2*x)*_C1+_C2*x^2*exp(2*x)+_C3*exp(2*x)*x