What is the solution for 64y^{''}-144y^'+81y=0 ?

The solution for 64y^{''}-144y^'+81y=0 is y=c_{1}e^{(9t)/8}+c_{2}e^{(9t)/8}t

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64y^{''}-144y^'+81y=0

64 y^{^{''}} - 144 y^{^{'}} + 81 y = 0

y = c_{1} e^{\frac{9 t}{8}} + c_{2} e^{\frac{9 t}{8}} t

Solution steps

64 y^{''} (t) - 144 y^{'} (t) + 81 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{9 t}{8}} + c_{2} e^{\frac{9 t}{8}} t

y = c_{1} e^{\frac{9 t}{8}} + c_{2} e^{\frac{9 t}{8}} t

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, (1) y = e^{2 x}

y^{^{''}} + 5 y^{^{'}} - 50 y = 0

y^{^{''}} - 440 y = 0

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (- 1) = 3

y^{^{''}} + 5 y = 0

What is the solution for 64y^{''}-144y^'+81y=0 ?
The solution for 64y^{''}-144y^'+81y=0 is y=c_{1}e^{(9t)/8}+c_{2}e^{(9t)/8}t