What is the solution for y^{''}+11y^'+28y=84x^2+66x+6+40e^x ?

The solution for y^{''}+11y^'+28y=84x^2+66x+6+40e^x is y=c_{1}e^{-4x}+c_{2}e^{-7x}+3x^2+e^x

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y^{''}+11y^'+28y=84x^2+66x+6+40e^x

y^{^{''}} + 11 y^{^{'}} + 28 y = 84 x^{2} + 66 x + 6 + 40 e^{x}

y = c_{1} e^{- 4 x} + c_{2} e^{- 7 x} + 3 x^{2} + e^{x}

Solution steps

y^{''} (x) + 11 y^{'} (x) + 28 y = 84 x^{2} + 66 x + 6 + 40 e^{x}

Solve linear ODE:

y = c_{1} e^{- 4 x} + c_{2} e^{- 7 x} + 3 x^{2} + e^{x}

y = c_{1} e^{- 4 x} + c_{2} e^{- 7 x} + 3 x^{2} + e^{x}

x \to 12 lim (x - 3)

f (x) = x^{2} - 3, at x = - 2

\int \frac{x}{2 x ^{2} + 5} d x

\int \frac{3 x + 1}{x ^{2} + x - 6} d x

x = 7 y^{2}, x = 3 + 4 y^{2}

What is the solution for y^{''}+11y^'+28y=84x^2+66x+6+40e^x ?
The solution for y^{''}+11y^'+28y=84x^2+66x+6+40e^x is y=c_{1}e^{-4x}+c_{2}e^{-7x}+3x^2+e^x