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 = 0.177262 (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 = 0.018 (sec), leaf count = 32
\[\left [y \left (x \right ) = {\mathrm e}^{2 x} \textit {\_C2} +{\mathrm e}^{3 x} \textit {\_C1} +\frac {{\mathrm e}^{a x}}{a^{2}-5 a +6}\right ]\] 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))
Maple raw output
[y(x) = exp(2*x)*_C2+exp(3*x)*_C1+1/(a^2-5*a+6)*exp(a*x)]