What is the solution for (d^2y)/(dt^2)-2(dy)/(dt)-15y=0 ?

The solution for (d^2y)/(dt^2)-2(dy)/(dt)-15y=0 is y=c_{1}e^{5t}+c_{2}e^{-3t}

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(d^2y)/(dt^2)-2(dy)/(dt)-15y=0

\frac{d ^{2} y}{d t ^{2}} - 2 \frac{d y}{d t} - 15 y = 0

y = c_{1} e^{5 t} + c_{2} e^{- 3 t}

Solution steps

\frac{d ^{2} y}{d t ^{2}} - 2 \frac{d y}{d t} - 15 y = 0

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{- 3 t}

y = c_{1} e^{5 t} + c_{2} e^{- 3 t}

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

20 y^{^{''}} + 9 y^{^{'}} + y = 0

x^{^{''}} + 4 x = 0, x (0) = 8, x^{^{'}} (0) = - 13

\frac{d ^{2} y}{d x ^{2}} = n y

4 y^{^{''}} + 9 y^{^{'}} - 9 y = 0

What is the solution for (d^2y)/(dt^2)-2(dy)/(dt)-15y=0 ?
The solution for (d^2y)/(dt^2)-2(dy)/(dt)-15y=0 is y=c_{1}e^{5t}+c_{2}e^{-3t}