ODE
\[ y''(x)+8 y'(x)+16 y(x)=4 e^x-e^{2 x} \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0371696 (sec), leaf count = 35
\[\left \{\left \{y(x)\to e^{-4 x} \left (c_2 x+c_1\right )+\frac {4 e^x}{25}-\frac {e^{2 x}}{36}\right \}\right \}\]
Maple ✓
cpu = 0.023 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-4\,x}}{\it \_C2}+{{\rm e}^{-4\,x}}x{\it \_C1}+{\frac {4\,{{\rm e}^{x}}}{25}}-{\frac {{{\rm e}^{2\,x}}}{36}} \right \} \] Mathematica raw input
DSolve[16*y[x] + 8*y'[x] + y''[x] == 4*E^x - E^(2*x),y[x],x]
Mathematica raw output
{{y[x] -> (4*E^x)/25 - E^(2*x)/36 + (C[1] + x*C[2])/E^(4*x)}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+8*diff(y(x),x)+16*y(x) = 4*exp(x)-exp(2*x), y(x),'implicit')
Maple raw output
y(x) = exp(-4*x)*_C2+exp(-4*x)*x*_C1+4/25*exp(x)-1/36*exp(2*x)