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

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

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

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

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + a y (x) = 0

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + 5 y = 0

4 y^{^{''}} + 20 y^{^{'}} + 169 y = 0, y (0) = 3, y^{^{'}} (0) = 1

4 y^{^{''}} - 10 y^{^{'}} = 0

y^{^{'''}} + 4 y^{^{''}} - 12 y^{^{'}} = 0

y^{^{''}} - 6 y^{^{'}} - 9 y = 0

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