What is the solution for (d^2y)/(dt^2)-6(dy)/(dt)-7y=0 ?

The solution for (d^2y)/(dt^2)-6(dy)/(dt)-7y=0 is y=c_{1}e^{7t}+c_{2}e^{-t}

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(d^2y)/(dt^2)-6(dy)/(dt)-7y=0

\frac{d ^{2} y}{d t ^{2}} - 6 \frac{d y}{d t} - 7 y = 0

y = c_{1} e^{7 t} + c_{2} e^{- t}

Solution steps

\frac{d ^{2} y}{d t ^{2}} - 6 \frac{d y}{d t} - 7 y = 0

Solve linear ODE:

y = c_{1} e^{7 t} + c_{2} e^{- t}

y = c_{1} e^{7 t} + c_{2} e^{- t}

x^{^{''}} = - 2 x

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

\frac{d ^{2} y}{d t ^{2}} - 1 \frac{d y}{d t} = 0

x^{^{''}} = - 4 x

y^{^{''}} - 12 y^{^{'}} + 36 y = 0, y (0) = 4, y^{^{'}} (0) = 15.45

What is the solution for (d^2y)/(dt^2)-6(dy)/(dt)-7y=0 ?
The solution for (d^2y)/(dt^2)-6(dy)/(dt)-7y=0 is y=c_{1}e^{7t}+c_{2}e^{-t}