What is the solution for 49y^{''}+126y^'+81y=0 ?

The solution for 49y^{''}+126y^'+81y=0 is y=c_{1}e^{-(9t)/7}+c_{2}e^{-(9t)/7}t

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49y^{''}+126y^'+81y=0

49 y^{^{''}} + 126 y^{^{'}} + 81 y = 0

y = c_{1} e^{- \frac{9 t}{7}} + c_{2} e^{- \frac{9 t}{7}} t

Solution steps

49 y^{''} (t) + 126 y^{'} (t) + 81 y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{9 t}{7}} + c_{2} e^{- \frac{9 t}{7}} t

y = c_{1} e^{- \frac{9 t}{7}} + c_{2} e^{- \frac{9 t}{7}} t

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What is the solution for 49y^{''}+126y^'+81y=0 ?
The solution for 49y^{''}+126y^'+81y=0 is y=c_{1}e^{-(9t)/7}+c_{2}e^{-(9t)/7}t