What is the solution for y^{''}+3y^'+2y=7cos(x)-sin(x) ?

The solution for y^{''}+3y^'+2y=7cos(x)-sin(x) is y=c_{1}e^{-x}+c_{2}e^{-2x}+2sin(x)+cos(x)

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y^{''}+3y^'+2y=7cos(x)-sin(x)

y^{^{''}} + 3 y^{^{'}} + 2 y = 7 cos (x) - sin (x)

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

Solution steps

y^{''} (x) + 3 y^{'} (x) + 2 y = 7 cos (x) - sin (x)

Solve linear ODE:

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

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

What is the solution for y^{''}+3y^'+2y=7cos(x)-sin(x) ?
The solution for y^{''}+3y^'+2y=7cos(x)-sin(x) is y=c_{1}e^{-x}+c_{2}e^{-2x}+2sin(x)+cos(x)