What is the solution for y^{''}-3y^'-54y=0 ?

The solution for y^{''}-3y^'-54y=0 is y=c_{1}e^{9t}+c_{2}e^{-6t}

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y^{''}-3y^'-54y=0

y^{^{''}} - 3 y^{^{'}} - 54 y = 0

y = c_{1} e^{9 t} + c_{2} e^{- 6 t}

Solution steps

y^{''} (t) - 3 y^{'} (t) - 54 y = 0

Solve linear ODE:

y = c_{1} e^{9 t} + c_{2} e^{- 6 t}

y = c_{1} e^{9 t} + c_{2} e^{- 6 t}

\frac{d}{d x} (x^{8 c o s (x)})

\int - \frac{x}{1 - x} d x

y = - x^{3} + 9 x^{2} - 6 x + 9, (7, 65)

y^{^{'}} = \frac{4 x ^{3} + 1}{2 y - 6}

\frac{d}{d t} (\frac{t sin ( t )}{1 + t})

What is the solution for y^{''}-3y^'-54y=0 ?
The solution for y^{''}-3y^'-54y=0 is y=c_{1}e^{9t}+c_{2}e^{-6t}