What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)-5y=0 ?

The solution for (d^2y)/(dx^2)-4(dy)/(dx)-5y=0 is y=c_{1}e^{5x}+c_{2}e^{-x}

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(d^2y)/(dx^2)-4(dy)/(dx)-5y=0

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 5 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 5 y = 0

Solve linear ODE:

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

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

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

8 y^{^{''}} + 80 y^{^{'}} + 128 y = 0, y (0) = 5, y^{^{'}} (0) = 8

u^{^{''}} + H (t) = 0, H (0) = 0, u^{^{'}} (0) = 2

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

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} = 0

What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)-5y=0 ?
The solution for (d^2y)/(dx^2)-4(dy)/(dx)-5y=0 is y=c_{1}e^{5x}+c_{2}e^{-x}