What is the solution for (d^2y)/(dx^2)+100y=0 ?

The solution for (d^2y)/(dx^2)+100y=0 is y=c_{1}cos(10x)+c_{2}sin(10x)

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(d^2y)/(dx^2)+100y=0

\frac{d ^{2} y}{d x ^{2}} + 100 y = 0

y = c_{1} cos (10 x) + c_{2} sin (10 x)

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 100 y = 0

Solve linear ODE:

y = c_{1} cos (10 x) + c_{2} sin (10 x)

y = c_{1} cos (10 x) + c_{2} sin (10 x)

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 12 y = 0

4 y^{^{''}} + 17 y = 0, y (0) = 3, y^{^{'}} (0) = 5

y^{^{''}} + 2 y^{^{'}} + 4 y = 0, y (0) = 1

y^{^{''}} + 2 y^{^{'}} + 1 y = 0, y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 3, y^{^{'}} (0) = - 7

What is the solution for (d^2y)/(dx^2)+100y=0 ?
The solution for (d^2y)/(dx^2)+100y=0 is y=c_{1}cos(10x)+c_{2}sin(10x)