What is the solution for (d^2y)/(dt^2)+7(dy)/(dt)+12y=0 ?

The solution for (d^2y)/(dt^2)+7(dy)/(dt)+12y=0 is y=c_{1}e^{-3t}+c_{2}e^{-4t}

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(d^2y)/(dt^2)+7(dy)/(dt)+12y=0

\frac{d ^{2} y}{d t ^{2}} + 7 \frac{d y}{d t} + 12 y = 0

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t}

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 7 \frac{d y}{d t} + 12 y = 0

Solve linear ODE:

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t}

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t}

\frac{d ^{2} y}{d t ^{2}} - 18 \frac{d y}{d t} + 145 y = 0

y^{^{'''}} - 3 y^{^{''}} - 15 y^{^{'}} + 25 y = 0

y^{^{''}} + 14 y^{^{'}} + 48 y = 0, y (0) = 0, y^{^{'}} (0) = - 6

y^{^{''}} + 6 y^{^{'}} + 25 y = 0, y (0) = 4, y^{^{'}} (0) = 5

2 y^{^{''}} + 50 y = 0, y (0) = 8, y^{^{'}} (0) = 35

What is the solution for (d^2y)/(dt^2)+7(dy)/(dt)+12y=0 ?
The solution for (d^2y)/(dt^2)+7(dy)/(dt)+12y=0 is y=c_{1}e^{-3t}+c_{2}e^{-4t}