What is the solution for -(d^2y)/(dx^2)+400y=0 ?

The solution for -(d^2y)/(dx^2)+400y=0 is y=c_{1}e^{20x}+c_{2}e^{-20x}

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-(d^2y)/(dx^2)+400y=0

- \frac{d ^{2} y}{d x ^{2}} + 400 y = 0

y = c_{1} e^{20 x} + c_{2} e^{- 20 x}

Solution steps

- \frac{d ^{2} y}{d x ^{2}} + 400 y = 0

Solve linear ODE:

y = c_{1} e^{20 x} + c_{2} e^{- 20 x}

y = c_{1} e^{20 x} + c_{2} e^{- 20 x}

y^{^{''}} + 4 y - 5 y = 0

y^{^{''}} - 2 y = 0, y (0) = 1, y^{^{'}} (0) = 6

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = - 1, y^{^{'}} (0) = - \frac{9}{4}

y^{^{''}} + 25 y = 0, y^{^{'}} (π) = 0, y^{^{'}} (0) = 0

10 y^{^{''}} + 6 y^{^{'}} + 10.9 y = 0

What is the solution for -(d^2y)/(dx^2)+400y=0 ?
The solution for -(d^2y)/(dx^2)+400y=0 is y=c_{1}e^{20x}+c_{2}e^{-20x}