What is the solution for y^{''}-8y^'-16y=0 ?

The solution for y^{''}-8y^'-16y=0 is y=c_{1}e^{4(1+sqrt(2))t}+c_{2}e^{4(1-sqrt(2))t}

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y^{''}-8y^'-16y=0

y^{^{''}} - 8 y^{^{'}} - 16 y = 0

y = c_{1} e^{4 (1 + 2) t} + c_{2} e^{4 (1 - 2) t}

Solution steps

y^{''} (t) - 8 y^{'} (t) - 16 y = 0

Solve linear ODE:

y = c_{1} e^{4 (1 + 2) t} + c_{2} e^{4 (1 - 2) t}

y = c_{1} e^{4 (1 + 2) t} + c_{2} e^{4 (1 - 2) t}

16 y^{^{''}} - 72 y^{^{'}} + 81 y = 0, y (0) = 8

y^{^{'''}} - 2 y^{^{''}} - 40 y^{^{'}} - 64 y = 0

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 29 y = 0

x^{^{''}} + 2 x^{^{'}} + 26 x = 0

\frac{d ^{2} f}{d x ^{2}} + k^{2} f (x) = 0

What is the solution for y^{''}-8y^'-16y=0 ?
The solution for y^{''}-8y^'-16y=0 is y=c_{1}e^{4(1+sqrt(2))t}+c_{2}e^{4(1-sqrt(2))t}