What is the solution for y^{''}+6y^'-27y=0 ?

The solution for y^{''}+6y^'-27y=0 is y=c_{1}e^{3t}+c_{2}e^{-9t}

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y^{''}+6y^'-27y=0

y^{^{''}} + 6 y^{^{'}} - 27 y = 0

y = c_{1} e^{3 t} + c_{2} e^{- 9 t}

Solution steps

y^{''} (t) + 6 y^{'} (t) - 27 y = 0

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 9 t}

y = c_{1} e^{3 t} + c_{2} e^{- 9 t}

\int \frac{x}{( 4 - 2 x ^{2} ) ^{3}} d x

\int \frac{x + 9}{x ^{2} + 4 x + 8} d x

\frac{d}{d x} (\frac{1}{3} x^{3} + \frac{1}{2} x^{2} - 6 x + 8)

\int x^{2} x^{3} + 35 d x

\frac{d}{d x} (1 + 1 - x)

What is the solution for y^{''}+6y^'-27y=0 ?
The solution for y^{''}+6y^'-27y=0 is y=c_{1}e^{3t}+c_{2}e^{-9t}