What is the solution for (d^2y)/(dx^2)+225y=0 ?

The solution for (d^2y)/(dx^2)+225y=0 is y=c_{1}cos(15x)+c_{2}sin(15x)

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(d^2y)/(dx^2)+225y=0

\frac{d ^{2} y}{d x ^{2}} + 225 y = 0

y = c_{1} cos (15 x) + c_{2} sin (15 x)

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 225 y = 0

Solve linear ODE:

y = c_{1} cos (15 x) + c_{2} sin (15 x)

y = c_{1} cos (15 x) + c_{2} sin (15 x)

y^{^{'''}} - 27 y = 0, y (0) = - 1, y^{^{'}} (0) = 6, y^{^{'''}} (0) = 18

y^{^{'''}} - 8 y = 0, y (0) = 1, y^{^{'}} (0) = - 1, y^{^{''}} (0) = 0

x^{^{''}} + 42.1788 x^{^{'}} + 295.2064 x = 0

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

4 y^{^{''}} + 44 y^{^{'}} + 121 y = 0

What is the solution for (d^2y)/(dx^2)+225y=0 ?
The solution for (d^2y)/(dx^2)+225y=0 is y=c_{1}cos(15x)+c_{2}sin(15x)