What is the solution for (d^2y)/(dt^2)-18(dy)/(dt)+145y=0 ?

The solution for (d^2y)/(dt^2)-18(dy)/(dt)+145y=0 is y=e^{9t}(c_{1}cos(8t)+c_{2}sin(8t))

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(d^2y)/(dt^2)-18(dy)/(dt)+145y=0

\frac{d ^{2} y}{d t ^{2}} - 18 \frac{d y}{d t} + 145 y = 0

y = e^{9 t} (c_{1} cos (8 t) + c_{2} sin (8 t))

Solution steps

\frac{d ^{2} y}{d t ^{2}} - 18 \frac{d y}{d t} + 145 y = 0

Solve linear ODE:

y = e^{9 t} (c_{1} cos (8 t) + c_{2} sin (8 t))

y = e^{9 t} (c_{1} cos (8 t) + c_{2} sin (8 t))

What is the solution for (d^2y)/(dt^2)-18(dy)/(dt)+145y=0 ?
The solution for (d^2y)/(dt^2)-18(dy)/(dt)+145y=0 is y=e^{9t}(c_{1}cos(8t)+c_{2}sin(8t))