What is the solution for 81y^{''}+72y^'+16y=0,y(0)=5,y^'(0)=-1 ?

The solution for 81y^{''}+72y^'+16y=0,y(0)=5,y^'(0)=-1 is y=5e^{-(4t)/9}+(11e^{-(4t)/9}t)/(9)

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81y^{''}+72y^'+16y=0,y(0)=5,y^'(0)=-1

81 y^{^{''}} + 72 y^{^{'}} + 16 y = 0, y (0) = 5, y^{^{'}} (0) = - 1

y = 5 e^{- \frac{4 t}{9}} + \frac{11 e ^{- \frac{4 t}{9}} t}{9}

Solution steps

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

Solve linear ODE:

y = 5 e^{- \frac{4 t}{9}} + \frac{11 e ^{- \frac{4 t}{9}} t}{9}

y = 5 e^{- \frac{4 t}{9}} + \frac{11 e ^{- \frac{4 t}{9}} t}{9}

What is the solution for 81y^{''}+72y^'+16y=0,y(0)=5,y^'(0)=-1 ?
The solution for 81y^{''}+72y^'+16y=0,y(0)=5,y^'(0)=-1 is y=5e^{-(4t)/9}+(11e^{-(4t)/9}t)/(9)