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

The solution for 4y^{''}+12y^'+9y=0,y(0)=1,y^'(0)=-4 is y=e^{-(3t)/2}-(5e^{-(3t)/2}t)/(2)

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

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

y = e^{- \frac{3 t}{2}} - \frac{5 e ^{- \frac{3 t}{2}} t}{2}

Solution steps

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

Solve linear ODE:

y = e^{- \frac{3 t}{2}} - \frac{5 e ^{- \frac{3 t}{2}} t}{2}

y = e^{- \frac{3 t}{2}} - \frac{5 e ^{- \frac{3 t}{2}} t}{2}

What is the solution for 4y^{''}+12y^'+9y=0,y(0)=1,y^'(0)=-4 ?
The solution for 4y^{''}+12y^'+9y=0,y(0)=1,y^'(0)=-4 is y=e^{-(3t)/2}-(5e^{-(3t)/2}t)/(2)