What is the solution for (d^2y)/(dx^2)+5^2y=0 ?

The solution for (d^2y)/(dx^2)+5^2y=0 is y=c_{1}cos(5x)+c_{2}sin(5x)

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(d^2y)/(dx^2)+5^2y=0

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

y = c_{1} cos (5 x) + c_{2} sin (5 x)

Solution steps

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

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x)

y = c_{1} cos (5 x) + c_{2} sin (5 x)

y^{^{''}} + 6 y^{^{'}} + 13 y = 0, y (0) = 3

2 y^{^{''}} + 9 y^{^{'}} - 5 y = 0

y^{^{''}} + 1 y = 0, y (π^{2}) = 3, y^{^{'}} (π^{2}) = - 1

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

8 x^{^{''}} + 20 x^{^{'}} + 32 x = 0

What is the solution for (d^2y)/(dx^2)+5^2y=0 ?
The solution for (d^2y)/(dx^2)+5^2y=0 is y=c_{1}cos(5x)+c_{2}sin(5x)