What is the solution for 2y^{''}+6y^'+8y=0 ?

The solution for 2y^{''}+6y^'+8y=0 is y=e^{-(3t)/2}(c_{1}cos((sqrt(7)t)/2)+c_{2}sin((sqrt(7)t)/2))

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2y^{''}+6y^'+8y=0

2 y^{^{''}} + 6 y^{^{'}} + 8 y = 0

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2}))

Solution steps

2 y^{''} (t) + 6 y^{'} (t) + 8 y = 0

Solve linear ODE:

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2}))

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2}))

What is the solution for 2y^{''}+6y^'+8y=0 ?
The solution for 2y^{''}+6y^'+8y=0 is y=e^{-(3t)/2}(c_{1}cos((sqrt(7)t)/2)+c_{2}sin((sqrt(7)t)/2))