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

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

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

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

y = c_{1} e^{6 t} + c_{2}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2}

y = c_{1} e^{6 t} + c_{2}

y^{^{'''}} + 7 y^{^{'}} = 0

x^{^{''}} = b x

y^{^{''}} + \frac{16}{3} y^{^{'}} + a y = 0, y (0) = 1, y^{^{'}} (0) = - \frac{4}{3}

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

y^{^{'''}} + 2 y^{^{''}} + 5 y^{^{'}} - 26 y = 0, y (0) = e^{2 x}

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