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

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

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(d^2y)/(dx^2)-25y=0

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

y = c_{1} e^{5 x} + c_{2} e^{- 5 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- 5 x}

y = c_{1} e^{5 x} + c_{2} e^{- 5 x}

9 y^{^{''}} + 6 y^{^{'}} + 82 y = 0, y (0) = 2

y^{^{''}} - 9 y = 0, y (0) = 2, y^{^{'}} (0) = 4

(4 D^{2} - 3 D - 10) y = 0

x^{^{'''}} - 4 x^{^{''}} - 3 x^{^{'}} + 18 x = 0

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

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