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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

\frac{5}{8} x^{^{''}} + 80 x = 0

\frac{d ^{2} x}{d t ^{2}} = - 4 x

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 12 y = 0

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 37 y = 0

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