What is the solution for 2y^{'''}-6y^{''}=x^2 ?

The solution for 2y^{'''}-6y^{''}=x^2 is y=c_{1}e^{3x}+c_{2}+c_{3}x-(x^4)/(72)-(x^3)/(54)-(x^2)/(54)

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2y^{'''}-6y^{''}=x^2

2 y^{^{'''}} - 6 y^{^{''}} = x^{2}

y = c_{1} e^{3 x} + c_{2} + c_{3} x - \frac{x ^{4}}{72} - \frac{x ^{3}}{54} - \frac{x ^{2}}{54}

Solution steps

2 y^{'''} (x) - 6 y^{''} (x) = x^{2}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} + c_{3} x - \frac{x ^{4}}{72} - \frac{x ^{3}}{54} - \frac{x ^{2}}{54}

y = c_{1} e^{3 x} + c_{2} + c_{3} x - \frac{x ^{4}}{72} - \frac{x ^{3}}{54} - \frac{x ^{2}}{54}

2 y^{^{''}} + 4 y^{^{'}} + 7 y = x^{2}

y^{^{''}} + 4 y^{^{'}} = 16 x

y^{^{'''}} - y^{^{''}} - 25 y^{^{'}} + 25 y = 3 - e^{x} + e^{5 x}

y^{^{''}} - 4 y^{^{'}} + 3 y = 2 x + 1

\frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} = - 3

What is the solution for 2y^{'''}-6y^{''}=x^2 ?
The solution for 2y^{'''}-6y^{''}=x^2 is y=c_{1}e^{3x}+c_{2}+c_{3}x-(x^4)/(72)-(x^3)/(54)-(x^2)/(54)