What is the solution for y^{''}-10y^'+61y=0 ?

The solution for y^{''}-10y^'+61y=0 is y=e^{5t}(c_{1}cos(6t)+c_{2}sin(6t))

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y^{''}-10y^'+61y=0

y^{^{''}} - 10 y^{^{'}} + 61 y = 0

y = e^{5 t} (c_{1} cos (6 t) + c_{2} sin (6 t))

Solution steps

y^{''} (t) - 10 y^{'} (t) + 61 y = 0

Solve linear ODE:

y = e^{5 t} (c_{1} cos (6 t) + c_{2} sin (6 t))

y = e^{5 t} (c_{1} cos (6 t) + c_{2} sin (6 t))

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

y^{^{'''}} + 4 y^{^{''}} - 28 y^{^{'}} + 32 y = 0

y^{^{'''}} - 9 y^{^{''}} = 0

y^{^{''}} - 5 y^{^{'}} + 7 y = 0

2 y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 1, y^{^{'}} (0) = - 5

What is the solution for y^{''}-10y^'+61y=0 ?
The solution for y^{''}-10y^'+61y=0 is y=e^{5t}(c_{1}cos(6t)+c_{2}sin(6t))