What is the solution for 9y^{''}+42y^'+49y=0 ?

The solution for 9y^{''}+42y^'+49y=0 is y=c_{1}e^{-(7t)/3}+c_{2}e^{-(7t)/3}t

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9y^{''}+42y^'+49y=0

9 y^{^{''}} + 42 y^{^{'}} + 49 y = 0

y = c_{1} e^{- \frac{7 t}{3}} + c_{2} e^{- \frac{7 t}{3}} t

Solution steps

9 y^{''} (t) + 42 y^{'} (t) + 49 y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{7 t}{3}} + c_{2} e^{- \frac{7 t}{3}} t

y = c_{1} e^{- \frac{7 t}{3}} + c_{2} e^{- \frac{7 t}{3}} t

\frac{d}{d x} (a + b x + c x^{2} + d x^{3})

x \to 7 lim (- 11)

x^{- \frac{1}{9}}

\frac{\partial}{\partial x} (5 x y^{4})

\frac{\partial}{\partial y} (\frac{13}{2} x^{4} y)

What is the solution for 9y^{''}+42y^'+49y=0 ?
The solution for 9y^{''}+42y^'+49y=0 is y=c_{1}e^{-(7t)/3}+c_{2}e^{-(7t)/3}t