ODE
\[ y''(x)-5 y'(x)+6 y(x)=e^{a x} \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0206845 (sec), leaf count = 54
\[\left \{\left \{y(x)\to \frac {e^{2 x} \left (\left (a^2-5 a+6\right ) c_2 e^x+\left (a^2-5 a+6\right ) c_1+e^{(a-2) x}\right )}{(a-3) (a-2)}\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 32
\[ \left \{ y \left ( x \right ) ={{\rm e}^{3\,x}}{\it \_C2}+{{\rm e}^{2\,x}}{\it \_C1}+{\frac {{{\rm e}^{ax}}}{{a}^{2}-5\,a+6}} \right \} \] Mathematica raw input
DSolve[6*y[x] - 5*y'[x] + y''[x] == E^(a*x),y[x],x]
Mathematica raw output
{{y[x] -> (E^(2*x)*(E^((-2 + a)*x) + (6 - 5*a + a^2)*C[1] + (6 - 5*a + a^2)*E^x*C[2]))/((-3 + a)*(-2 + a))}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-5*diff(y(x),x)+6*y(x) = exp(a*x), y(x),'implicit')
Maple raw output
y(x) = exp(3*x)*_C2+exp(2*x)*_C1+1/(a^2-5*a+6)*exp(a*x)