What is the solution for 100y^{''}+90y^'-162y=0 ?

The solution for 100y^{''}+90y^'-162y=0 is y=c_{1}e^{(9t}{10}}+c_{2}e^{-\frac{9t)/5}

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100y^{''}+90y^'-162y=0

100 y^{^{''}} + 90 y^{^{'}} - 162 y = 0

y = c_{1} e^{\frac{9 t}{10}} + c_{2} e^{- \frac{9 t}{5}}

Solution steps

100 y^{''} (t) + 90 y^{'} (t) - 162 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{9 t}{10}} + c_{2} e^{- \frac{9 t}{5}}

y = c_{1} e^{\frac{9 t}{10}} + c_{2} e^{- \frac{9 t}{5}}

y^{^{''}} - 4 y^{^{'}} - 13 y = 0

\frac{3}{4} \frac{d ^{2} x}{d t ^{2}} + 72 x = 0, x (0) = - \frac{1}{2}

y^{^{''}} - 16 y^{^{'}} + 73 y = 0

y^{^{''}} - 8 y^{^{'}} + 9 y = 0, y (0) = 0, y^{^{'}} (0) = 3

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

What is the solution for 100y^{''}+90y^'-162y=0 ?
The solution for 100y^{''}+90y^'-162y=0 is y=c_{1}e^{(9t}{10}}+c_{2}e^{-\frac{9t)/5}