What is the solution for y^{''}+10y^'+25y=50sin(5x) ?

The solution for y^{''}+10y^'+25y=50sin(5x) is y=c_{1}e^{-5x}+c_{2}xe^{-5x}-cos(5x)

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y^{''}+10y^'+25y=50sin(5x)

y^{^{''}} + 10 y^{^{'}} + 25 y = 50 sin (5 x)

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

Solution steps

y^{''} (x) + 10 y^{'} (x) + 25 y = 50 sin (5 x)

Solve linear ODE:

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

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

What is the solution for y^{''}+10y^'+25y=50sin(5x) ?
The solution for y^{''}+10y^'+25y=50sin(5x) is y=c_{1}e^{-5x}+c_{2}xe^{-5x}-cos(5x)