What is the solution for 81y^{''}+72y^'+16y=0,y(0)=2,y^'(0)=-1 ?

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

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81y^{''}+72y^'+16y=0,y(0)=2,y^'(0)=-1

81 y^{^{''}} + 72 y^{^{'}} + 16 y = 0, y (0) = 2, y^{^{'}} (0) = - 1

y = 2 e^{- \frac{4 t}{9}} - \frac{e ^{- \frac{4 t}{9}} t}{9}

Solution steps

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

Solve linear ODE:

y = 2 e^{- \frac{4 t}{9}} - \frac{e ^{- \frac{4 t}{9}} t}{9}

y = 2 e^{- \frac{4 t}{9}} - \frac{e ^{- \frac{4 t}{9}} t}{9}

\int_{1}^{2} (\frac{3}{x ^{2}} - 1) d x

\frac{d y}{d x} = \frac{2 x + y + 1}{4 x + 2 y - 5}

x \to 0 lim (5 + 4 x - x^{3})

x \to - \infty lim (4)

x \to \infty lim (3 \cdot 2^{x})

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