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

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

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

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

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 25 \cdot 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}

x^{^{''}} = - x^{^{'}} + 3 x

y^{^{'''}} - 7 y^{^{''}} + 14 y^{^{'}} - 8 y = 0

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

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

y^{^{''}} - 6 y^{^{'}} + 32 y = 0

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