What is the solution for 2y^{'''}-3y^{''}+y=x^2+x ?

The solution for 2y^{'''}-3y^{''}+y=x^2+x is y=c_{1}e^{-x/2}+c_{2}e^x+c_{3}xe^x+x^2+x+6

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

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

y = c_{1} e^{- \frac{x}{2}} + c_{2} e^{x} + c_{3} x e^{x} + x^{2} + x + 6

Solution steps

2 y^{'''} (x) - 3 y^{''} (x) + y = x^{2} + x

Solve linear ODE:

y = c_{1} e^{- \frac{x}{2}} + c_{2} e^{x} + c_{3} x e^{x} + x^{2} + x + 6

y = c_{1} e^{- \frac{x}{2}} + c_{2} e^{x} + c_{3} x e^{x} + x^{2} + x + 6

y^{^{''}} + 4 y^{^{'}} + 5 y = 50 x + 13 e^{3 x}

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

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

y^{^{'''}} - y^{^{'}} = 10 sin (3 x)

y^{^{''}} + 4 y^{^{'}} + 4 y = 2 e^{- 2 x}

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