What is the solution for (d^2y)/(dt^2)-2(dy)/(dt)-3y=0 ?

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

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(d^2y)/(dt^2)-2(dy)/(dt)-3y=0

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 5 y^{^{'}} - 50 y = 0

8 y^{^{''}} - 14 y^{^{'}} + 3 y = 0

y^{^{''}} - 12 y^{^{'}} + 32 y = 0, y (0) = 1, y^{^{'}} (0) = 4

y^{^{''''}} - 34 y^{^{'''}} + 289 y^{^{''}} = 0

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

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