What is the solution for 49y^{''}+126y^'+97y=0 ?

The solution for 49y^{''}+126y^'+97y=0 is y=e^{-(9t)/7}(c_{1}cos((4t)/7)+c_{2}sin((4t)/7))

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49y^{''}+126y^'+97y=0

49 y^{^{''}} + 126 y^{^{'}} + 97 y = 0

y = e^{- \frac{9 t}{7}} (c_{1} cos (\frac{4 t}{7}) + c_{2} sin (\frac{4 t}{7}))

Solution steps

49 y^{''} (t) + 126 y^{'} (t) + 97 y = 0

Solve linear ODE:

y = e^{- \frac{9 t}{7}} (c_{1} cos (\frac{4 t}{7}) + c_{2} sin (\frac{4 t}{7}))

y = e^{- \frac{9 t}{7}} (c_{1} cos (\frac{4 t}{7}) + c_{2} sin (\frac{4 t}{7}))

\frac{1}{d ^{7}}

h (x) = (4 x + 6)^{x}

x \to - 2 lim (3^{x^{2 + 1}})

\int_{0}^{4} \frac{1}{x ^{2} - 4 x - 5} d x

\frac{d}{d x} (8 x^{\frac{2}{3}} + x^{\frac{5}{3}})

What is the solution for 49y^{''}+126y^'+97y=0 ?
The solution for 49y^{''}+126y^'+97y=0 is y=e^{-(9t)/7}(c_{1}cos((4t)/7)+c_{2}sin((4t)/7))