What is the solution for 16y^{''}+56y^'+49y=0,y(0)=5 ?

The solution for 16y^{''}+56y^'+49y=0,y(0)=5 is y=5e^{-(7t)/4}+c_{2}e^{-(7t)/4}t

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16y^{''}+56y^'+49y=0,y(0)=5

16 y^{^{''}} + 56 y^{^{'}} + 49 y = 0, y (0) = 5

y = 5 e^{- \frac{7 t}{4}} + c_{2} e^{- \frac{7 t}{4}} t

Solution steps

16 y^{''} (t) + 56 y^{'} (t) + 49 y = 0

Solve linear ODE:

y = 5 e^{- \frac{7 t}{4}} + c_{2} e^{- \frac{7 t}{4}} t

y = 5 e^{- \frac{7 t}{4}} + c_{2} e^{- \frac{7 t}{4}} t

What is the solution for 16y^{''}+56y^'+49y=0,y(0)=5 ?
The solution for 16y^{''}+56y^'+49y=0,y(0)=5 is y=5e^{-(7t)/4}+c_{2}e^{-(7t)/4}t