What is the solution for y^{''}+2y^'+3/4 y=0 ?

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

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y^{''}+2y^'+3/4 y=0

y^{^{''}} + 2 y^{^{'}} + \frac{3}{4} y = 0

y = c_{1} e^{- \frac{t}{2}} + c_{2} e^{- \frac{3 t}{2}}

Solution steps

y^{''} (t) + 2 y^{'} (t) + \frac{3}{4} y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{t}{2}} + c_{2} e^{- \frac{3 t}{2}}

y = c_{1} e^{- \frac{t}{2}} + c_{2} e^{- \frac{3 t}{2}}

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