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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 64 y = 0

3 y^{^{''}} + 11 y^{^{'}} - 7 y = 0

y^{^{''}} - 6 y^{^{'}} - 16 y = 0, y (0) = 3, y^{^{'}} (0) = 4

y^{^{''}} + y^{^{'}} + y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 5, y^{^{'}} (0) = 3

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