What is the solution for 4y^{''}+12y^'+9y=0,y(0)=3,y^'(0)=5 ?

The solution for 4y^{''}+12y^'+9y=0,y(0)=3,y^'(0)=5 is y=3e^{-(3t)/2}+(19e^{-(3t)/2}t)/(2)

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4y^{''}+12y^'+9y=0,y(0)=3,y^'(0)=5

4 y^{^{''}} + 12 y^{^{'}} + 9 y = 0, y (0) = 3, y^{^{'}} (0) = 5

y = 3 e^{- \frac{3 t}{2}} + \frac{19 e ^{- \frac{3 t}{2}} t}{2}

Solution steps

4 y^{''} (t) + 12 y^{'} (t) + 9 y = 0

Solve linear ODE:

y = 3 e^{- \frac{3 t}{2}} + \frac{19 e ^{- \frac{3 t}{2}} t}{2}

y = 3 e^{- \frac{3 t}{2}} + \frac{19 e ^{- \frac{3 t}{2}} t}{2}

y^{^{''''}} + 5 y^{^{''}} - 36 y = 0

y^{^{''}} + 16 y = 0, y (\frac{π}{8}) = - 2, y^{^{'}} (\frac{π}{8}) = 16

y^{^{'''}} + 2 y^{^{''}} - 15 y^{^{'}} - 36 y = 0

y^{^{''}} + 8 y^{^{'}} + 6 y = 0, y (- 1) = 6, y^{^{'}} (- 1) = 5

2 y^{^{''}} + 4 y^{^{'}} + 20 y = 0

What is the solution for 4y^{''}+12y^'+9y=0,y(0)=3,y^'(0)=5 ?
The solution for 4y^{''}+12y^'+9y=0,y(0)=3,y^'(0)=5 is y=3e^{-(3t)/2}+(19e^{-(3t)/2}t)/(2)