What is the solution for 9y^{''}+2y^'-y=15 ?

The solution for 9y^{''}+2y^'-y=15 is y=c_{1}e^{((-1+sqrt(10))t)/9}+c_{2}e^{-((1+sqrt(10))t)/9}-15

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9y^{''}+2y^'-y=15

9 y^{^{''}} + 2 y^{^{'}} - y = 15

y = c_{1} e^{\frac{( - 1 + 10 ) t}{9}} + c_{2} e^{- \frac{( 1 + 10 ) t}{9}} - 15

Solution steps

9 y^{''} (t) + 2 y^{'} (t) - y = 15

Solve linear ODE:

y = c_{1} e^{\frac{( - 1 + 10 ) t}{9}} + c_{2} e^{- \frac{( 1 + 10 ) t}{9}} - 15

y = c_{1} e^{\frac{( - 1 + 10 ) t}{9}} + c_{2} e^{- \frac{( 1 + 10 ) t}{9}} - 15

y^{^{''}} - y^{^{'}} = 1, y (0) = 18, y^{^{'}} (0) = 1

y^{^{''}} + 5 y = (x)

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = 12 e^{x}

y^{^{''}} - y^{^{'}} = 8 - (t - 2)

x^{^{''}} - 16 x^{^{'}} + 64 x = 5 t e^{8 t}

What is the solution for 9y^{''}+2y^'-y=15 ?
The solution for 9y^{''}+2y^'-y=15 is y=c_{1}e^{((-1+sqrt(10))t)/9}+c_{2}e^{-((1+sqrt(10))t)/9}-15