What is the solution for y^{''}-6y^'+90y=0 ?

The solution for y^{''}-6y^'+90y=0 is y=e^{3t}(c_{1}cos(9t)+c_{2}sin(9t))

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y^{''}-6y^'+90y=0

y^{^{''}} - 6 y^{^{'}} + 90 y = 0

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

Solution steps

y^{''} (t) - 6 y^{'} (t) + 90 y = 0

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 9 y = 0

y^{^{''}} + 20 y^{^{'}} + 100 y = 0

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (- 1) = 5

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y^{0} = 1, y^{^{'}} 0 = 0

y^{^{''}} - 2 π y^{^{'}} + π^{2} y = 0

What is the solution for y^{''}-6y^'+90y=0 ?
The solution for y^{''}-6y^'+90y=0 is y=e^{3t}(c_{1}cos(9t)+c_{2}sin(9t))