What is the solution for y^{''}-16y^'-63y=0 ?

The solution for y^{''}-16y^'-63y=0 is y=c_{1}e^{(8+sqrt(127))t}+c_{2}e^{(8-sqrt(127))t}

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y^{''}-16y^'-63y=0

y^{^{''}} - 16 y^{^{'}} - 63 y = 0

y = c_{1} e^{(8 + 127) t} + c_{2} e^{(8 - 127) t}

Solution steps

y^{''} (t) - 16 y^{'} (t) - 63 y = 0

Solve linear ODE:

y = c_{1} e^{(8 + 127) t} + c_{2} e^{(8 - 127) t}

y = c_{1} e^{(8 + 127) t} + c_{2} e^{(8 - 127) t}

y^{^{''}} + \frac{3}{2} y^{^{'}} + \frac{3}{8} y = 0

5 \frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} - 90 y = 0

y^{^{''}} - 9 y = 0, y^{^{'}} (0) = 0

y^{^{''}} - 25 y = 0, y (0) = 1, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} = 0

What is the solution for y^{''}-16y^'-63y=0 ?
The solution for y^{''}-16y^'-63y=0 is y=c_{1}e^{(8+sqrt(127))t}+c_{2}e^{(8-sqrt(127))t}