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

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

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

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

y = c_{1} e^{7 t} + c_{2}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{7 t} + c_{2}

y = c_{1} e^{7 t} + c_{2}

y^{^{''}} + 4 y^{^{'}} - 5 y = 0, y (ln (2)) = 3, y (0) = 33

y^{^{'''}} - 4 y^{^{''}} - 45 y^{^{'}} = 0

y^{^{''}} - y = 0, y^{0} = 2

y^{^{'''}} - 5 y^{^{''}} + 5 y^{^{'}} + 11 y = 0

36 y^{^{''}} + 108 y^{^{'}} + 97 y = 0, y^{^{'}} (1) = 3, y (1) = 4

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