What is the solution for 16y^{''}-72y^'+81y=0 ?

The solution for 16y^{''}-72y^'+81y=0 is y=c_{1}e^{(9t)/4}+c_{2}e^{(9t)/4}t

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16y^{''}-72y^'+81y=0

16 y^{^{''}} - 72 y^{^{'}} + 81 y = 0

y = c_{1} e^{\frac{9 t}{4}} + c_{2} e^{\frac{9 t}{4}} t

Solution steps

16 y^{''} (t) - 72 y^{'} (t) + 81 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{9 t}{4}} + c_{2} e^{\frac{9 t}{4}} t

y = c_{1} e^{\frac{9 t}{4}} + c_{2} e^{\frac{9 t}{4}} t

y^{^{''''}} - 2 y^{^{''}} - 8 y = 0

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

y^{^{'''}} + y^{^{''}} - 30 y^{^{'}} = 0

θ^{^{''}} (t) + 16.33 θ (t) = 0

y^{^{''}} + c^{2} y = 0

What is the solution for 16y^{''}-72y^'+81y=0 ?
The solution for 16y^{''}-72y^'+81y=0 is y=c_{1}e^{(9t)/4}+c_{2}e^{(9t)/4}t