What is the solution for y^{''}-4y^'-7y=0 ?

The solution for y^{''}-4y^'-7y=0 is y=c_{1}e^{(2+sqrt(11))t}+c_{2}e^{(2-sqrt(11))t}

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y^{''}-4y^'-7y=0

y^{^{''}} - 4 y^{^{'}} - 7 y = 0

y = c_{1} e^{(2 + 11) t} + c_{2} e^{(2 - 11) t}

Solution steps

y^{''} (t) - 4 y^{'} (t) - 7 y = 0

Solve linear ODE:

y = c_{1} e^{(2 + 11) t} + c_{2} e^{(2 - 11) t}

y = c_{1} e^{(2 + 11) t} + c_{2} e^{(2 - 11) t}

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = \frac{3}{4}

y^{^{''}} + 4 y^{^{'}} + cy = 0, y (0) = 1, y^{^{'}} (0) = - \frac{10}{3}

(D^{2} + 8 D + 16) y = 0

y^{^{''}} - \frac{1}{9} y = 0

y^{^{'''}} + y^{^{''}} - 6 y^{^{'}} = 0 y

What is the solution for y^{''}-4y^'-7y=0 ?
The solution for y^{''}-4y^'-7y=0 is y=c_{1}e^{(2+sqrt(11))t}+c_{2}e^{(2-sqrt(11))t}