ODE
\[ y''(x)-5 y'(x)+6 y(x)=4 e^x x^2 \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.210199 (sec), leaf count = 33
\[\left \{\left \{y(x)\to e^x \left (2 x^2+6 x+c_1 e^x+c_2 e^{2 x}+7\right )\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 30
\[[y \left (x \right ) = {\mathrm e}^{2 x} \textit {\_C2} +{\mathrm e}^{3 x} \textit {\_C1} +\left (2 x^{2}+6 x +7\right ) {\mathrm e}^{x}]\] Mathematica raw input
DSolve[6*y[x] - 5*y'[x] + y''[x] == 4*E^x*x^2,y[x],x]
Mathematica raw output
{{y[x] -> E^x*(7 + 6*x + 2*x^2 + E^x*C[1] + E^(2*x)*C[2])}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-5*diff(y(x),x)+6*y(x) = 4*x^2*exp(x), y(x))
Maple raw output
[y(x) = exp(2*x)*_C2+exp(3*x)*_C1+(2*x^2+6*x+7)*exp(x)]