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

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

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xy^{'''}+2y^{''}=6x

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

y = c_{1} x + c_{2} + c_{3} ln (x) + \frac{x ^{3}}{3}

Solution steps

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

Solve linear ODE:

y = c_{1} x + c_{2} + c_{3} ln (x) + \frac{x ^{3}}{3}

y = c_{1} x + c_{2} + c_{3} ln (x) + \frac{x ^{3}}{3}

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\frac{d}{d x} (\frac{x ^{2} + 5}{x ^{2} - 1})

\frac{d}{d x} (2 x^{2} + 4 x - 1)

\int_{0}^{1} \frac{61}{4 y - 1} d y

\frac{d y}{d x}, ln (x^{2} - 24 y) = x - y - 4

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