What is the solution for (d^2y)/(dx^2)+36y=0 ?

The solution for (d^2y)/(dx^2)+36y=0 is y=c_{1}cos(6x)+c_{2}sin(6x)

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(d^2y)/(dx^2)+36y=0

\frac{d ^{2} y}{d x ^{2}} + 36 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 36 y = 0

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)

x^{^{''}} - 2 x^{^{'}} + 5 x = 0

y^{^{''}} + 49 y = 0, y (0) = 5, y^{^{'}} (0) = - 7

y^{^{''}} + y = 0, y (π) = 0, y (0) = 0

y^{^{''}} - 13 y^{^{'}} + 42 y = 0

x^{^{''}} + 2 \cdot x^{^{'}} + 10 x = 0

What is the solution for (d^2y)/(dx^2)+36y=0 ?
The solution for (d^2y)/(dx^2)+36y=0 is y=c_{1}cos(6x)+c_{2}sin(6x)