What is the solution for 16y^{''}+152y^'+361y=0,y(0)=9,y^'(0)=2 ?

The solution for 16y^{''}+152y^'+361y=0,y(0)=9,y^'(0)=2 is y=9e^{-(19t)/4}+(179e^{-(19t)/4}t)/(4)

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16y^{''}+152y^'+361y=0,y(0)=9,y^'(0)=2

16 y^{^{''}} + 152 y^{^{'}} + 361 y = 0, y (0) = 9, y^{^{'}} (0) = 2

y = 9 e^{- \frac{19 t}{4}} + \frac{179 e ^{- \frac{19 t}{4}} t}{4}

Solution steps

16 y^{''} (t) + 152 y^{'} (t) + 361 y = 0

Solve linear ODE:

y = 9 e^{- \frac{19 t}{4}} + \frac{179 e ^{- \frac{19 t}{4}} t}{4}

y = 9 e^{- \frac{19 t}{4}} + \frac{179 e ^{- \frac{19 t}{4}} t}{4}

\frac{\partial}{\partial y} (ln (1 + x^{2} + y))

\int \frac{18}{( x ^{2} - 1 ) ^{2}} d x

y^{^{'}} + 7 x^{- 1} y = x^{2}

10 arcsin (e^{\frac{x}{2}})

\int \frac{4 x ^{2}}{x ^{2} + 7} d x

What is the solution for 16y^{''}+152y^'+361y=0,y(0)=9,y^'(0)=2 ?
The solution for 16y^{''}+152y^'+361y=0,y(0)=9,y^'(0)=2 is y=9e^{-(19t)/4}+(179e^{-(19t)/4}t)/(4)