What is the solution for 63x^2y^{''}+14x(x-9)y^'-14(x-9)y=-2x^3 ?

The solution for 63x^2y^{''}+14x(x-9)y^'-14(x-9)y=-2x^3 is y=c_{1}x+c_{2}e^{-(2x)/9}x-(x^2)/7

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63x^2y^{''}+14x(x-9)y^'-14(x-9)y=-2x^3

63 x^{2} y^{^{''}} + 14 x (x - 9) y^{^{'}} - 14 (x - 9) y = - 2 x^{3}

y = c_{1} x + c_{2} e^{- \frac{2 x}{9}} x - \frac{x ^{2}}{7}

Solution steps

63 x^{2} y^{''} (x) + 14 x (x - 9) y^{'} (x) - 14 (x - 9) y = - 2 x^{3}

Solve using substitution:

y = c_{1} x + c_{2} e^{- \frac{2 x}{9}} x - \frac{x ^{2}}{7}

y = c_{1} x + c_{2} e^{- \frac{2 x}{9}} x - \frac{x ^{2}}{7}

What is the solution for 63x^2y^{''}+14x(x-9)y^'-14(x-9)y=-2x^3 ?
The solution for 63x^2y^{''}+14x(x-9)y^'-14(x-9)y=-2x^3 is y=c_{1}x+c_{2}e^{-(2x)/9}x-(x^2)/7