What is the solution for y^{''}-8y^{''}-9y=0 ?

The solution for y^{''}-8y^{''}-9y=0 is y=c_{1}cos((3t)/(sqrt(7)))+c_{2}sin((3t)/(sqrt(7)))

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y^{''}-8y^{''}-9y=0

y^{^{''}} - 8 y^{^{''}} - 9 y = 0

y = c_{1} cos (\frac{3 t}{7}) + c_{2} sin (\frac{3 t}{7})

Solution steps

y^{''} (t) - 8 y^{''} (t) - 9 y = 0

Solve linear ODE:

y = c_{1} cos (\frac{3 t}{7}) + c_{2} sin (\frac{3 t}{7})

y = c_{1} cos (\frac{3 t}{7}) + c_{2} sin (\frac{3 t}{7})

y^{^{''}} + 3 y^{^{'}} + 2 y = 0, y (0) = \frac{1}{4}

y^{^{''}} + (3 - a) y^{^{'}} + 2 (a - 1) y = 0

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} - 64 y = 0

\frac{10}{32} y^{^{''}} + \frac{1}{6} y = 0, y (0) = \frac{1}{6}, y^{^{'}} (0) = - 1

10000 y^{^{''}} - 729 y = 0, y (0) = 9

What is the solution for y^{''}-8y^{''}-9y=0 ?
The solution for y^{''}-8y^{''}-9y=0 is y=c_{1}cos((3t)/(sqrt(7)))+c_{2}sin((3t)/(sqrt(7)))