4.29.14 \(4 y''(x)-2 y'(x)-y(x)=0\)

ODE
\[ 4 y''(x)-2 y'(x)-y(x)=0 \] ODE Classification

[[_2nd_order, _missing_x]]

Book solution method
TO DO

Mathematica
cpu = 0.00617189 (sec), leaf count = 38

\[\left \{\left \{y(x)\to e^{-\frac {1}{4} \left (\sqrt {5}-1\right ) x} \left (c_2 e^{\frac {\sqrt {5} x}{2}}+c_1\right )\right \}\right \}\]

Maple
cpu = 0.004 (sec), leaf count = 27

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{{\frac { \left ( \sqrt {5}+1 \right ) x}{4}}}}+{\it \_C2}\,{{\rm e}^{-{\frac { \left ( \sqrt {5}-1 \right ) x}{4}}}} \right \} \] Mathematica raw input

DSolve[-y[x] - 2*y'[x] + 4*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (C[1] + E^((Sqrt[5]*x)/2)*C[2])/E^(((-1 + Sqrt[5])*x)/4)}}

Maple raw input

dsolve(4*diff(diff(y(x),x),x)-2*diff(y(x),x)-y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*exp(1/4*(5^(1/2)+1)*x)+_C2*exp(-1/4*(5^(1/2)-1)*x)