What is the solution for y^{''}-4y^'+11y=0 ?

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

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y^{''}-4y^'+11y=0

y^{^{''}} - 4 y^{^{'}} + 11 y = 0

y = e^{2 t} (c_{1} cos (7 t) + c_{2} sin (7 t))

Solution steps

y^{''} (t) - 4 y^{'} (t) + 11 y = 0

Solve linear ODE:

y = e^{2 t} (c_{1} cos (7 t) + c_{2} sin (7 t))

y = e^{2 t} (c_{1} cos (7 t) + c_{2} sin (7 t))

\frac{y ^{^{''}}}{y ^{^{'}}} = 1

y^{^{''}} + 2 y^{^{'}} + y = 0, y (1) = 6, y^{^{'}} (0) = 6

y^{^{'''}} - 13 y^{^{''}} + 12 y^{^{'}} = 0

y^{^{''}} - 5 y + 6 y = 0, y (0) = - \frac{3}{5}, y^{^{'}} (0) = - \frac{13}{5}

5 y^{^{''}} + 9 y^{^{'}} = 0

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