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 = 0.0301625 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \frac {(a-1)^2 e^{a x} \left (c_2 x+c_1\right )+e^x}{(a-1)^2}\right \}\right \}\]
Maple ✓
cpu = 0.017 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) ={\frac { \left ( a-1 \right ) ^{2} \left ( {\it \_C1}\,x+{\it \_C2} \right ) {{\rm e}^{ax}}+{{\rm e}^{x}}}{ \left ( a-1 \right ) ^{2}}} \right \} \] 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]))/(-1 + a)^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),'implicit')
Maple raw output
y(x) = ((a-1)^2*(_C1*x+_C2)*exp(a*x)+exp(x))/(a-1)^2