What is the solution for y^{''}+5y^'-6y=36x+98xe^x ?

The solution for y^{''}+5y^'-6y=36x+98xe^x is y=c_{1}e^x+c_{2}e^{-6x}-6x-5+7x^2e^x-2e^xx

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y^{''}+5y^'-6y=36x+98xe^x

y^{^{''}} + 5 y^{^{'}} - 6 y = 36 x + 98 x e^{x}

y = c_{1} e^{x} + c_{2} e^{- 6 x} - 6 x - 5 + 7 x^{2} e^{x} - 2 e^{x} x

Solution steps

y^{''} (x) + 5 y^{'} (x) - 6 y = 36 x + 98 x e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 6 x} - 6 x - 5 + 7 x^{2} e^{x} - 2 e^{x} x

y = c_{1} e^{x} + c_{2} e^{- 6 x} - 6 x - 5 + 7 x^{2} e^{x} - 2 e^{x} x

y^{^{''}} + 49 y = 49 sec^{2} (7 t)

y^{^{''}} - y^{^{'}} = - 2

4 y + 7 y^{^{'}} + 2 y^{^{''}} = 10 \cdot cos (4 x)

y^{^{''}} - y^{^{'}} + y = sin (t) - 3 e^{2 t}

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

What is the solution for y^{''}+5y^'-6y=36x+98xe^x ?
The solution for y^{''}+5y^'-6y=36x+98xe^x is y=c_{1}e^x+c_{2}e^{-6x}-6x-5+7x^2e^x-2e^xx