What is the solution for y^{''}-9y^'+81y=0 ?

The solution for y^{''}-9y^'+81y=0 is y=e^{(9t)/2}(c_{1}cos((9sqrt(3)t)/2)+c_{2}sin((9sqrt(3)t)/2))

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y^{''}-9y^'+81y=0

y^{^{''}} - 9 y^{^{'}} + 81 y = 0

y = e^{\frac{9 t}{2}} (c_{1} cos (\frac{9 3 t}{2}) + c_{2} sin (\frac{9 3 t}{2}))

Solution steps

y^{''} (t) - 9 y^{'} (t) + 81 y = 0

Solve linear ODE:

y = e^{\frac{9 t}{2}} (c_{1} cos (\frac{9 3 t}{2}) + c_{2} sin (\frac{9 3 t}{2}))

y = e^{\frac{9 t}{2}} (c_{1} cos (\frac{9 3 t}{2}) + c_{2} sin (\frac{9 3 t}{2}))

y^{^{''}} + 4 \cdot y = 0

y^{^{''}} - 6 y^{^{'}} - 216 y = 0

u^{^{''}} + 7 H (t) = 0, H (0) = 0, u^{^{'}} (0) = 7

y^{^{''}} + 4 y^{^{'}} + 13 y^{^{'}} = 0

y \cdot α + \frac{d ^{2} y}{d x ^{2}} = 0

What is the solution for y^{''}-9y^'+81y=0 ?
The solution for y^{''}-9y^'+81y=0 is y=e^{(9t)/2}(c_{1}cos((9sqrt(3)t)/2)+c_{2}sin((9sqrt(3)t)/2))