What is the solution for (d^2y)/(dx^2)=-36y ?

The solution for (d^2y)/(dx^2)=-36y is y=c_{1}cos(6x)+c_{2}sin(6x)

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(d^2y)/(dx^2)=-36y

\frac{d ^{2} y}{d x ^{2}} = - 36 y

y = c_{1} cos (6 x) + c_{2} sin (6 x)

Solution steps

\frac{d ^{2} y}{d x ^{2}} = - 36 y

Solve linear ODE:

y = c_{1} cos (6 x) + c_{2} sin (6 x)

y = c_{1} cos (6 x) + c_{2} sin (6 x)

y^{^{''}} - 6 y^{^{'}} + 25 y = 0, y (0) = - 3, y^{^{'}} (0) = - 1

y^{^{''}} + \frac{100}{1} y^{^{'}} = 0

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

y^{^{''}} = 2 y + y^{^{'}}

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

What is the solution for (d^2y)/(dx^2)=-36y ?
The solution for (d^2y)/(dx^2)=-36y is y=c_{1}cos(6x)+c_{2}sin(6x)