What is the solution for 9y^{''}-12y+4y=0 ?

The solution for 9y^{''}-12y+4y=0 is y=c_{1}e^{(2^{3/2}t)/3}+c_{2}e^{-(2^{3/2}t)/3}

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9y^{''}-12y+4y=0

9 y^{^{''}} - 12 y + 4 y = 0

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

Solution steps

9 y^{''} (t) - 12 y + 4 y = 0

Solve linear ODE:

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

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

y^{^{''''}} - 16 y^{^{'''}} + 64 y^{^{''}} = 0

2 y^{^{''}} + 36 y^{^{'}} + 163 y = 0, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} + 8 y^{^{'}} - 9 y = 0, y (1) = 1

x^{^{''}} + 2 x^{^{'}} + 3 x = 0

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = 2, y^{^{'}} (0) = 10

What is the solution for 9y^{''}-12y+4y=0 ?
The solution for 9y^{''}-12y+4y=0 is y=c_{1}e^{(2^{3/2}t)/3}+c_{2}e^{-(2^{3/2}t)/3}