What is the solution for y^{''}-14y^'+51y=0 ?

The solution for y^{''}-14y^'+51y=0 is y=e^{7t}(c_{1}cos(sqrt(2)t)+c_{2}sin(sqrt(2)t))

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y^{''}-14y^'+51y=0

y^{^{''}} - 14 y^{^{'}} + 51 y = 0

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

Solution steps

y^{''} (t) - 14 y^{'} (t) + 51 y = 0

Solve linear ODE:

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

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

x y^{^{'}} + y = - 8 x y^{2}, y (1) = 1

\int \frac{7 x}{x ^{2} + 4} d x

(3 cos (x))^{^{'}}

\frac{\partial}{\partial x} (x^{3} y^{2} - 2 x e^{x y})

\int cot (y) csc^{2} (y) d y

What is the solution for y^{''}-14y^'+51y=0 ?
The solution for y^{''}-14y^'+51y=0 is y=e^{7t}(c_{1}cos(sqrt(2)t)+c_{2}sin(sqrt(2)t))