What is the solution for (d^2y)/(dx^2)+49y=0 ?

The solution for (d^2y)/(dx^2)+49y=0 is y=c_{1}cos(7x)+c_{2}sin(7x)

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(d^2y)/(dx^2)+49y=0

\frac{d ^{2} y}{d x ^{2}} + 49 y = 0

y = c_{1} cos (7 x) + c_{2} sin (7 x)

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 49 y = 0

Solve linear ODE:

y = c_{1} cos (7 x) + c_{2} sin (7 x)

y = c_{1} cos (7 x) + c_{2} sin (7 x)

y^{^{''''}} - 32 y^{^{'''}} + 256 y^{^{''}} = 0

y^{^{''''''}} - 729 y = 0

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

x^{^{''}} + 4 x^{^{'}} + 3 x = 0

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

What is the solution for (d^2y)/(dx^2)+49y=0 ?
The solution for (d^2y)/(dx^2)+49y=0 is y=c_{1}cos(7x)+c_{2}sin(7x)