What is the solution for y^{''}+5y^'=100sin(5t)+150cos(5t) ?

The solution for y^{''}+5y^'=100sin(5t)+150cos(5t) is y=c_{1}+c_{2}e^{-5t}+sin(5t)-5cos(5t)

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y^{''}+5y^'=100sin(5t)+150cos(5t)

y^{^{''}} + 5 y^{^{'}} = 100 sin (5 t) + 150 cos (5 t)

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

Solution steps

y^{''} (t) + 5 y^{'} (t) = 100 sin (5 t) + 150 cos (5 t)

Solve linear ODE:

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

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

y^{^{''}} + 49 y = - 5 cos (7 t + π^{3})

y^{^{''}} + b^{2} y = sin (b t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{'''}} - y^{^{'}} = 6 sin (t)

y^{^{''}} + 4 y^{^{'}} + 5 y = (e^{- 2 x}) sec (x)

y^{^{''}} + 6 y^{^{'}} + 8 y = e^{- 2 x} + sin (x)

What is the solution for y^{''}+5y^'=100sin(5t)+150cos(5t) ?
The solution for y^{''}+5y^'=100sin(5t)+150cos(5t) is y=c_{1}+c_{2}e^{-5t}+sin(5t)-5cos(5t)