What is the solution for (d^2y)/(dt^2)-5(dy)/(dt)=0 ?

The solution for (d^2y)/(dt^2)-5(dy)/(dt)=0 is y=c_{1}e^{5t}+c_{2}

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(d^2y)/(dt^2)-5(dy)/(dt)=0

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} = 0

y = c_{1} e^{5 t} + c_{2}

Solution steps

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} = 0

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2}

y = c_{1} e^{5 t} + c_{2}

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

\frac{4}{32} x^{^{''}} + x^{^{'}} + 2 x = 0, x (0) = - 1, x^{^{'}} (0) = 16

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} + 6 y = 0, y (1) = 3

x^{^{''}} - 3 x^{^{'}} = 0

y^{^{''}} + 36 y = 0, y (0) = 5, y^{^{'}} (0) = - 12

What is the solution for (d^2y)/(dt^2)-5(dy)/(dt)=0 ?
The solution for (d^2y)/(dt^2)-5(dy)/(dt)=0 is y=c_{1}e^{5t}+c_{2}