What is the solution for y^{''}+6y^'+5y=5x^3+13x^2+4x ?

The solution for y^{''}+6y^'+5y=5x^3+13x^2+4x is y=c_{1}e^{-x}+c_{2}e^{-5x}+x^3-x^2+2x-2

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y^{''}+6y^'+5y=5x^3+13x^2+4x

y^{^{''}} + 6 y^{^{'}} + 5 y = 5 x^{3} + 13 x^{2} + 4 x

y = c_{1} e^{- x} + c_{2} e^{- 5 x} + x^{3} - x^{2} + 2 x - 2

Solution steps

y^{''} (x) + 6 y^{'} (x) + 5 y = 5 x^{3} + 13 x^{2} + 4 x

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 5 x} + x^{3} - x^{2} + 2 x - 2

y = c_{1} e^{- x} + c_{2} e^{- 5 x} + x^{3} - x^{2} + 2 x - 2

y^{^{''''}} + 8 y^{^{''}} + 16 y = cos (3 x) + 5

y^{^{''}} - y^{^{'}} - 2 y = cos (2 t)

y^{^{''}} + 4 y = cos (9 x)

y^{^{''}} + 4 y = csc^{2} (2 x)

y^{^{''}} - 2 y^{^{'}} + y = 4 cos (t)

What is the solution for y^{''}+6y^'+5y=5x^3+13x^2+4x ?
The solution for y^{''}+6y^'+5y=5x^3+13x^2+4x is y=c_{1}e^{-x}+c_{2}e^{-5x}+x^3-x^2+2x-2