What is the solution for 81y^{''}+72y^'+16y=0,y^'(0)=-1 ?

The solution for 81y^{''}+72y^'+16y=0,y^'(0)=-1 is y=-(e^{-(4t)/9}(-9-9c_{2}))/(4)+c_{2}e^{-(4t)/9}t

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81y^{''}+72y^'+16y=0,y^'(0)=-1

81 y^{^{''}} + 72 y^{^{'}} + 16 y = 0, y^{^{'}} (0) = - 1

y = - \frac{e ^{- \frac{4 t}{9}} ( - 9 - 9 c _{2} )}{4} + c_{2} e^{- \frac{4 t}{9}} t

Solution steps

81 y^{''} (t) + 72 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = - \frac{e ^{- \frac{4 t}{9}} ( - 9 - 9 c _{2} )}{4} + c_{2} e^{- \frac{4 t}{9}} t

y = - \frac{e ^{- \frac{4 t}{9}} ( - 9 - 9 c _{2} )}{4} + c_{2} e^{- \frac{4 t}{9}} t

\frac{d}{d x} (x^{\frac{9}{4}} + e^{- 2 x})

2 \frac{d y}{d x} + 6 y + 4 = 0

f (x) = (3 x^{2} + 3 x - 1)^{4}

\int x \cdot sin (x) \cdot cos (x) d x

y = ln (\frac{4}{x})

What is the solution for 81y^{''}+72y^'+16y=0,y^'(0)=-1 ?
The solution for 81y^{''}+72y^'+16y=0,y^'(0)=-1 is y=-(e^{-(4t)/9}(-9-9c_{2}))/(4)+c_{2}e^{-(4t)/9}t