What is the solution for 25y^{''}+70y^'+49y=0 ?

The solution for 25y^{''}+70y^'+49y=0 is y=c_{1}e^{-(7t)/5}+c_{2}e^{-(7t)/5}t

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25y^{''}+70y^'+49y=0

25 y^{^{''}} + 70 y^{^{'}} + 49 y = 0

y = c_{1} e^{- \frac{7 t}{5}} + c_{2} e^{- \frac{7 t}{5}} t

Solution steps

25 y^{''} (t) + 70 y^{'} (t) + 49 y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{7 t}{5}} + c_{2} e^{- \frac{7 t}{5}} t

y = c_{1} e^{- \frac{7 t}{5}} + c_{2} e^{- \frac{7 t}{5}} t

y^{^{''}} - y^{^{'}} - 20 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

6 f^{^{''}} (t) = 3 f^{^{''}} (t) - 5 f (t)

y^{^{''}} - 6 y^{^{'}} + 16 y = 0

y^{^{''}} - 4 y^{^{'}} + 13 y = 0, y (0) = - 1, y^{^{'}} (0) = 5

3 y^{^{''}} + 2 y^{^{'}} + \frac{1}{4} y = 0

What is the solution for 25y^{''}+70y^'+49y=0 ?
The solution for 25y^{''}+70y^'+49y=0 is y=c_{1}e^{-(7t)/5}+c_{2}e^{-(7t)/5}t