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}

\frac{d}{d x} (\frac{x ^{4} + 3 x ^{2}}{( x ^{2} + 1 ) ^{2}})

\frac{\partial}{\partial x} (A)

x \to 1 lim (\frac{ln ( x )}{x})

- \frac{2}{x}

\int \frac{1}{x ^{2} ( x + 2 )} d x

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}