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

The solution for 49y^{''}+56y^'+16y=0 is y=c_{1}e^{-(4t)/7}+c_{2}e^{-(4t)/7}t

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49y^{''}+56y^'+16y=0

49 y^{^{''}} + 56 y^{^{'}} + 16 y = 0

y = c_{1} e^{- \frac{4 t}{7}} + c_{2} e^{- \frac{4 t}{7}} t

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- \frac{4 t}{7}} + c_{2} e^{- \frac{4 t}{7}} t

y = c_{1} e^{- \frac{4 t}{7}} + c_{2} e^{- \frac{4 t}{7}} t

y^{^{''}} + y^{^{'}} - 15 y = 0

6 y^{^{''''}} + 11 y^{^{''}} + 4 y = 0

y^{^{''''}} - 4 y^{^{'''}} + 5 y^{^{''}} - 4 y^{^{'}} + 4 y = 0

u^{^{''}} + 4 u^{^{'}} + 4 H (t) = 0

x^{^{''}} - 8 x = 0

What is the solution for 49y^{''}+56y^'+16y=0 ?
The solution for 49y^{''}+56y^'+16y=0 is y=c_{1}e^{-(4t)/7}+c_{2}e^{-(4t)/7}t