What is the solution for linear (d^2y)/(dx^2)+25y=0 ?

The solution for linear (d^2y)/(dx^2)+25y=0 is y=c_{1}cos(5x)+c_{2}sin(5x)

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linear (d^2y)/(dx^2)+25y=0

linear

\frac{d ^{2} y}{d x ^{2}} + 25 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 25 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^{^{''}} - y^{^{'}} - 20 y = 0, y (0) = 4, y^{^{'}} (0) = 29

y^{^{''}} - 8 y^{^{'}} + 2 y = 0

y^{^{''}} + 11 y^{^{'}} + 12 y = 0

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

y^{^{''}} + 4000 y^{^{'}} + 4000000 y = 0

What is the solution for linear (d^2y)/(dx^2)+25y=0 ?
The solution for linear (d^2y)/(dx^2)+25y=0 is y=c_{1}cos(5x)+c_{2}sin(5x)