What is the solution for y^{''}-12y^'-27y=0 ?

The solution for y^{''}-12y^'-27y=0 is y=c_{1}e^{3(2+sqrt(7))t}+c_{2}e^{3(2-sqrt(7))t}

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y^{''}-12y^'-27y=0

y^{^{''}} - 12 y^{^{'}} - 27 y = 0

y = c_{1} e^{3 (2 + 7) t} + c_{2} e^{3 (2 - 7) t}

Solution steps

y^{''} (t) - 12 y^{'} (t) - 27 y = 0

Solve linear ODE:

y = c_{1} e^{3 (2 + 7) t} + c_{2} e^{3 (2 - 7) t}

y = c_{1} e^{3 (2 + 7) t} + c_{2} e^{3 (2 - 7) t}

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

y^{^{'''''}} + 4 y^{^{''''}} + 4 y^{^{'''}} = 0

2 y^{^{''}} + 8 y^{^{'}} + 52 y = 0

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (1) = e^{3 x}

4 \frac{d ^{2} y}{d x ^{2}} - 16 \frac{d y}{d x} + 16 y = 0

What is the solution for y^{''}-12y^'-27y=0 ?
The solution for y^{''}-12y^'-27y=0 is y=c_{1}e^{3(2+sqrt(7))t}+c_{2}e^{3(2-sqrt(7))t}