What is the solution for y^{''}-2y^'+y=x+1 ?

The solution for y^{''}-2y^'+y=x+1 is y=c_{1}e^x+c_{2}xe^x+x+3

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y^{''}-2y^'+y=x+1

y^{^{''}} - 2 y^{^{'}} + y = x + 1

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

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = x + 1

Solve linear ODE:

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

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

y^{^{''}} + y = e^{- x} (2 sin (x) + 4 cos (x))

y^{^{''}} + y^{^{'}} - 7 y = 3 e^{2 x} - 2 e^{3 x}

y^{^{'''}} + y^{^{'}} - 10 = x e^{2 x}

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 2 (1 + e^{- x})

y^{^{''}} + y^{^{'}} - 2 y = 18 x e^{- 2 x} - 12 e^{- 2 x}

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