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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (- 1) = 2, y^{^{'}} (- 1) = 3

2 y^{^{''}} + 16 y^{^{'}} + 82 y = 0

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

121 y^{^{''}} + 198 y^{^{'}} + 80 y = 0

2 y^{^{'''}} + 7 y^{^{''}} + 4 y^{^{'}} - 4 y = 0

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