What is the solution for 81y^{''}+180y^'+100y=0 ?

The solution for 81y^{''}+180y^'+100y=0 is y=c_{1}e^{-(10t)/9}+c_{2}e^{-(10t)/9}t

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81y^{''}+180y^'+100y=0

81 y^{^{''}} + 180 y^{^{'}} + 100 y = 0

y = c_{1} e^{- \frac{10 t}{9}} + c_{2} e^{- \frac{10 t}{9}} t

Solution steps

81 y^{''} (t) + 180 y^{'} (t) + 100 y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{10 t}{9}} + c_{2} e^{- \frac{10 t}{9}} t

y = c_{1} e^{- \frac{10 t}{9}} + c_{2} e^{- \frac{10 t}{9}} t

\int_{0}^{20} 3 x d x

\int \frac{1}{t ^{2} 100 - t ^{2}} d t

x \to 0 lim (ln (cos (x)))

4 t y^{^{'}} + 4 = 5 + t

x \to 0 lim (0^{0})

What is the solution for 81y^{''}+180y^'+100y=0 ?
The solution for 81y^{''}+180y^'+100y=0 is y=c_{1}e^{-(10t)/9}+c_{2}e^{-(10t)/9}t