What is the solution for 5y^{''}-30y^'+170y=0 ?

The solution for 5y^{''}-30y^'+170y=0 is y=e^{3t}(c_{1}cos(5t)+c_{2}sin(5t))

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5y^{''}-30y^'+170y=0

5 y^{^{''}} - 30 y^{^{'}} + 170 y = 0

y = e^{3 t} (c_{1} cos (5 t) + c_{2} sin (5 t))

Solution steps

5 y^{''} (t) - 30 y^{'} (t) + 170 y = 0

Solve linear ODE:

y = e^{3 t} (c_{1} cos (5 t) + c_{2} sin (5 t))

y = e^{3 t} (c_{1} cos (5 t) + c_{2} sin (5 t))

y^{^{''}} + 14 y^{^{'}} + 49 y = 0, y (- 4) = 1, y^{^{'}} (- 4) = 5

y^{^{'''}} - 49 y^{^{'}} = 0

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} = - y

y^{^{''}} + 2 y^{^{'}} + 10 y = 0, y (0) = e^{- \frac{π}{6}}

\frac{d ^{3} y}{d t ^{3}} - \frac{d ^{2} y}{d t ^{2}} = 0

What is the solution for 5y^{''}-30y^'+170y=0 ?
The solution for 5y^{''}-30y^'+170y=0 is y=e^{3t}(c_{1}cos(5t)+c_{2}sin(5t))