What is the solution for y^{''}+15y^'+56y=112x^2+60x+4+72e^x ?

The solution for y^{''}+15y^'+56y=112x^2+60x+4+72e^x is y=c_{1}e^{-7x}+c_{2}e^{-8x}+2x^2+e^x

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y^{''}+15y^'+56y=112x^2+60x+4+72e^x

y^{^{''}} + 15 y^{^{'}} + 56 y = 112 x^{2} + 60 x + 4 + 72 e^{x}

y = c_{1} e^{- 7 x} + c_{2} e^{- 8 x} + 2 x^{2} + e^{x}

Solution steps

y^{''} (x) + 15 y^{'} (x) + 56 y = 112 x^{2} + 60 x + 4 + 72 e^{x}

Solve linear ODE:

y = c_{1} e^{- 7 x} + c_{2} e^{- 8 x} + 2 x^{2} + e^{x}

y = c_{1} e^{- 7 x} + c_{2} e^{- 8 x} + 2 x^{2} + e^{x}

(d^{3} - 3 d^{2} + 4 d - 2) y = e^{x} + cos (x) + x

y^{^{''}} - y = 2 e^{x} sinh (x)

y^{^{''}} + 16 y = 0.5 sin (4 t), y (0) = 0.5

(D^{2} + 9) y = 81 x^{2} + (14 cos (x))

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = t^{- 2} e^{2 t}

What is the solution for y^{''}+15y^'+56y=112x^2+60x+4+72e^x ?
The solution for y^{''}+15y^'+56y=112x^2+60x+4+72e^x is y=c_{1}e^{-7x}+c_{2}e^{-8x}+2x^2+e^x