What is the solution for y^{''}-6y^'+5y=5x^2+3x-16-9e^{2x} ?

The solution for y^{''}-6y^'+5y=5x^2+3x-16-9e^{2x} is y=c_{1}e^{5x}+c_{2}e^x+x^2+3x+3e^{2x}

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y^{''}-6y^'+5y=5x^2+3x-16-9e^{2x}

y^{^{''}} - 6 y^{^{'}} + 5 y = 5 x^{2} + 3 x - 16 - 9 e^{2 x}

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

Solution steps

y^{''} (x) - 6 y^{'} (x) + 5 y = 5 x^{2} + 3 x - 16 - 9 e^{2 x}

Solve linear ODE:

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

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

y^{^{''}} - 9 y = (x^{2} - 6) sin (3 x)

y^{^{''}} + y^{^{'}} - 2 y = 2 e^{x}

y^{^{''}} + y^{^{'}} - 6 y = 12 e^{3 t} + 12 e^{- 2 t}

y^{^{''}} + 3 y^{^{'}} = 2 x^{4}

y^{^{''}} + 5 y^{^{'}} + 2 y = e^{- x}

What is the solution for y^{''}-6y^'+5y=5x^2+3x-16-9e^{2x} ?
The solution for y^{''}-6y^'+5y=5x^2+3x-16-9e^{2x} is y=c_{1}e^{5x}+c_{2}e^x+x^2+3x+3e^{2x}