ODE
\[ y''(x)-\left (2 e^x+1\right ) y'(x)+e^{2 x} y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.170545 (sec), leaf count = 20
\[\left \{\left \{y(x)\to e^{e^x} \left (c_2 e^x+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.077 (sec), leaf count = 31
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{\frac {x}{2}+{\mathrm e}^{x}} \sinh \left (\frac {x}{2}\right )+\textit {\_C2} \,{\mathrm e}^{\frac {x}{2}+{\mathrm e}^{x}} \cosh \left (\frac {x}{2}\right )\right ]\] Mathematica raw input
DSolve[E^(2*x)*y[x] - (1 + 2*E^x)*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^E^x*(C[1] + E^x*C[2])}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-(1+2*exp(x))*diff(y(x),x)+exp(2*x)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(1/2*x+exp(x))*sinh(1/2*x)+_C2*exp(1/2*x+exp(x))*cosh(1/2*x)]