ODE
\[ 4 y''(x)-2 y'(x)-y(x)=0 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.159788 (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 = 0.007 (sec), leaf count = 27
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{\frac {\left (\sqrt {5}+1\right ) x}{4}}+\textit {\_C2} \,{\mathrm e}^{-\frac {\left (\sqrt {5}-1\right ) x}{4}}\right ]\] 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))
Maple raw output
[y(x) = _C1*exp(1/4*(5^(1/2)+1)*x)+_C2*exp(-1/4*(5^(1/2)-1)*x)]