What is the solution for (d^2y)/(dt^2)-8(dy)/(dt)+16y=0 ?

The solution for (d^2y)/(dt^2)-8(dy)/(dt)+16y=0 is y=c_{1}e^{4t}+c_{2}te^{4t}

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(d^2y)/(dt^2)-8(dy)/(dt)+16y=0

\frac{d ^{2} y}{d t ^{2}} - 8 \frac{d y}{d t} + 16 y = 0

y = c_{1} e^{4 t} + c_{2} t e^{4 t}

Solution steps

\frac{d ^{2} y}{d t ^{2}} - 8 \frac{d y}{d t} + 16 y = 0

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} t e^{4 t}

y = c_{1} e^{4 t} + c_{2} t e^{4 t}

3 y^{^{''}} - 2 y^{^{'}} - 7 y = 0

y^{^{''}} + y^{^{'}} + 9.5 y = 0

y^{^{''}} + 16 y = 0, y (π^{8}) = - 2, y^{^{'}} (π^{8}) = 16

y^{^{''}} - 3 y^{^{'}} - 4 y = 0, y (0) = 3, y (0) = 2

y^{^{''}} - \frac{10}{3} y^{^{'}} + α y = 0

What is the solution for (d^2y)/(dt^2)-8(dy)/(dt)+16y=0 ?
The solution for (d^2y)/(dt^2)-8(dy)/(dt)+16y=0 is y=c_{1}e^{4t}+c_{2}te^{4t}