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 = 0.0114033 (sec), leaf count = 33
\[\left \{\left \{y(x)\to e^x \left (c_1 e^x+c_2 e^{2 x}+2 x^2+6 x+7\right )\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) ={{\rm e}^{2\,x}}{\it \_C1}+{{\rm e}^{3\,x}}{\it \_C2}+2\,{{\rm e}^{x}} \left ( {x}^{2}+3\,x+7/2 \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = exp(2*x)*_C1+exp(3*x)*_C2+2*exp(x)*(x^2+3*x+7/2)