What is the solution for 324y^{''}+252y^'+49y=0,y(0)=9 ?

The solution for 324y^{''}+252y^'+49y=0,y(0)=9 is y=9e^{-(7t)/(18)}+c_{2}e^{-(7t)/(18)}t

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324y^{''}+252y^'+49y=0,y(0)=9

324 y^{^{''}} + 252 y^{^{'}} + 49 y = 0, y (0) = 9

y = 9 e^{- \frac{7 t}{18}} + c_{2} e^{- \frac{7 t}{18}} t

Solution steps

324 y^{''} (t) + 252 y^{'} (t) + 49 y = 0

Solve linear ODE:

y = 9 e^{- \frac{7 t}{18}} + c_{2} e^{- \frac{7 t}{18}} t

y = 9 e^{- \frac{7 t}{18}} + c_{2} e^{- \frac{7 t}{18}} t

y^{^{'''}} + 4 y^{^{''}} - 128 y = 0, y (0) = e^{4 x}

y^{^{''}} + 64 y = 0, y (0) = 0, y^{^{'}} (0) = \frac{1}{3}

y^{^{''}} - 2 y^{^{'}} + 5 y = 0, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 2 y^{^{'}} + 24 y = 0

y^{^{''}} - 9 y^{^{'}} + 5 y = 0

What is the solution for 324y^{''}+252y^'+49y=0,y(0)=9 ?
The solution for 324y^{''}+252y^'+49y=0,y(0)=9 is y=9e^{-(7t)/(18)}+c_{2}e^{-(7t)/(18)}t