What is the solution for 4y^{''}+12y^'+9y=0,y(0)=2,y^'(0)=-1 ?

The solution for 4y^{''}+12y^'+9y=0,y(0)=2,y^'(0)=-1 is y=2e^{-(3t)/2}+2e^{-(3t)/2}t

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4y^{''}+12y^'+9y=0,y(0)=2,y^'(0)=-1

4 y^{^{''}} + 12 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = - 1

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

Solution steps

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

Solve linear ODE:

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

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

x^{^{''}} + 3 x^{^{'}} - 3 x = 0

y^{^{''}} + 8 y^{^{'}} + 160 y = 0

0.1 y^{^{''}} + y^{^{'}} + y = 0, y (0) = 1, y (1) = 0

y^{^{''}} + 0.2 y^{^{'}} + 0.01 y = 0

y^{^{''}} + 9 y^{^{'}} - 20 y = 0, y (0) = 1, y^{^{'}} (0) = 2

What is the solution for 4y^{''}+12y^'+9y=0,y(0)=2,y^'(0)=-1 ?
The solution for 4y^{''}+12y^'+9y=0,y(0)=2,y^'(0)=-1 is y=2e^{-(3t)/2}+2e^{-(3t)/2}t