What is the solution for y^{''}-6y^'+13y=13 ?

The solution for y^{''}-6y^'+13y=13 is y=e^{3t}(c_{1}cos(2t)+c_{2}sin(2t))+1

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y^{''}-6y^'+13y=13

y^{^{''}} - 6 y^{^{'}} + 13 y = 13

y = e^{3 t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + 1

Solution steps

y^{''} (t) - 6 y^{'} (t) + 13 y = 13

Solve linear ODE:

y = e^{3 t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + 1

y = e^{3 t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + 1

y^{^{''}} + 4 y = 16 t

y^{^{''}} - 8 y^{^{'}} + 16 y = e^{4 t} ln (t)

10 y^{^{''}} + 1000 y = 100 cos (8 t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 9 y^{^{'}} + 14 y = 2 + t, y (0) = 1, y^{^{'}} (0) = 1

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 9 e^{- t} + 3

What is the solution for y^{''}-6y^'+13y=13 ?
The solution for y^{''}-6y^'+13y=13 is y=e^{3t}(c_{1}cos(2t)+c_{2}sin(2t))+1