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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

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

y^{^{''}} + 8 y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{'''}} - 2 y^{^{'}} - 13 y^{^{'}} - 10 y = 0

\frac{d ^{2} y}{d x ^{2}} + 0.6 \frac{d y}{d x} + 8 y = 0

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