What is the solution for 16*y^{''}+24*y^'+73*y=0,y(0)=[4] ?

The solution for 16*y^{''}+24*y^'+73*y=0,y(0)=[4] is y=e^{-(3t)/4}(4cos(2t)+c_{2}sin(2t))

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16y^{''}+24y^'+73*y=0,y(0)=[4]

16 \cdot y^{^{''}} + 24 \cdot y^{^{'}} + 73 \cdot y = 0, y (0) = [4]

y = e^{- \frac{3 t}{4}} (4 cos (2 t) + c_{2} sin (2 t))

Solution steps

16 \cdot y^{''} (t) + 24 \cdot y^{'} (t) + 73 \cdot y = 0

Solve linear ODE:

y = e^{- \frac{3 t}{4}} (4 cos (2 t) + c_{2} sin (2 t))

y = e^{- \frac{3 t}{4}} (4 cos (2 t) + c_{2} sin (2 t))

64 y^{^{''}} - 81 y = 0

y^{^{''}} + 4 y = 0, y (3 π) = - 3, y (0) = - 3

y^{^{''}} - y^{^{'}} = 0, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - y^{^{'}} = 0, y (0) = 0, y^{^{'}} (0) = 1

2 y^{^{''}} + 14 y^{^{'}} + 12 y = 0

What is the solution for 16*y^{''}+24*y^'+73*y=0,y(0)=[4] ?
The solution for 16*y^{''}+24*y^'+73*y=0,y(0)=[4] is y=e^{-(3t)/4}(4cos(2t)+c_{2}sin(2t))