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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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3 x^{2} y^{2} d x + y d y = 5 x y

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