What is the solution for y^{''}-18y^'+82y=0,y(0)=9,y^'(0)=4 ?

The solution for y^{''}-18y^'+82y=0,y(0)=9,y^'(0)=4 is y=e^{9t}(9cos(t)-77sin(t))

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y^{''}-18y^'+82y=0,y(0)=9,y^'(0)=4

y^{^{''}} - 18 y^{^{'}} + 82 y = 0, y (0) = 9, y^{^{'}} (0) = 4

y = e^{9 t} (9 cos (t) - 77 sin (t))

Solution steps

y^{''} (t) - 18 y^{'} (t) + 82 y = 0

Solve linear ODE:

y = e^{9 t} (9 cos (t) - 77 sin (t))

y = e^{9 t} (9 cos (t) - 77 sin (t))

(D^{5} - 6 D^{4} + 9 D^{3}) y = 0

y^{^{'''}} + y^{^{''}} + 3 y^{^{'}} - 5 y = 0

y^{^{''}} + 24 y^{^{'}} + a y = 0, y (0) = 1, y^{^{'}} (0) = - 22

y^{^{''}} - y = 0, y^{0} = 2, y^{^{'}} 0 = 6

y^{^{''}} + 7 y^{^{'}} + 12 y = 0, y (0) = 2, y^{^{'}} (0) = 1

What is the solution for y^{''}-18y^'+82y=0,y(0)=9,y^'(0)=4 ?
The solution for y^{''}-18y^'+82y=0,y(0)=9,y^'(0)=4 is y=e^{9t}(9cos(t)-77sin(t))