What is the solution for 36y^{''}+84y^'+49y=0 ?

The solution for 36y^{''}+84y^'+49y=0 is y=c_{1}e^{-(7t)/6}+c_{2}e^{-(7t)/6}t

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36y^{''}+84y^'+49y=0

36 y^{^{''}} + 84 y^{^{'}} + 49 y = 0

y = c_{1} e^{- \frac{7 t}{6}} + c_{2} e^{- \frac{7 t}{6}} t

Solution steps

36 y^{''} (t) + 84 y^{'} (t) + 49 y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{7 t}{6}} + c_{2} e^{- \frac{7 t}{6}} t

y = c_{1} e^{- \frac{7 t}{6}} + c_{2} e^{- \frac{7 t}{6}} t

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What is the solution for 36y^{''}+84y^'+49y=0 ?
The solution for 36y^{''}+84y^'+49y=0 is y=c_{1}e^{-(7t)/6}+c_{2}e^{-(7t)/6}t