ODE
\[ a^2 y(x)-2 a y'(x)+y''(x)=e^x \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.179447 (sec), leaf count = 28
\[\left \{\left \{y(x)\to \frac {e^x}{(a-1)^2}+e^{a x} (c_2 x+c_1)\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 26
\[\left [y \left (x \right ) = {\mathrm e}^{a x} \textit {\_C2} +x \,{\mathrm e}^{a x} \textit {\_C1} +\frac {{\mathrm e}^{x}}{\left (a -1\right )^{2}}\right ]\] Mathematica raw input
DSolve[a^2*y[x] - 2*a*y'[x] + y''[x] == E^x,y[x],x]
Mathematica raw output
{{y[x] -> E^x/(-1 + a)^2 + E^(a*x)*(C[1] + x*C[2])}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-2*a*diff(y(x),x)+a^2*y(x) = exp(x), y(x))
Maple raw output
[y(x) = exp(a*x)*_C2+x*exp(a*x)*_C1+exp(x)/(a-1)^2]