What is the solution for 4y^{''''}-y^{''}=6x-1 ?

The solution for 4y^{''''}-y^{''}=6x-1 is y=c_{1}e^{x/2}+c_{2}e^{-x/2}+c_{3}+c_{4}x-x^3+(x^2)/2

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4y^{''''}-y^{''}=6x-1

4 y^{^{''''}} - y^{^{''}} = 6 x - 1

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

Solution steps

4 y^{(4)} (x) - y^{''} (x) = 6 x - 1

Solve linear ODE:

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

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

y^{^{''}} + 4 y^{^{'}} + 3 y = e^{x}

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

(d^{2} + 1) y = csc (x)

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

y^{^{''}} + 1.44 y = 24 cos (1.2 x)

What is the solution for 4y^{''''}-y^{''}=6x-1 ?
The solution for 4y^{''''}-y^{''}=6x-1 is y=c_{1}e^{x/2}+c_{2}e^{-x/2}+c_{3}+c_{4}x-x^3+(x^2)/2