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

The solution for x^2y^{''}+2xy^'-6y=x^2-2 is y=c_{1}x^2+(c_{2})/(x^3)+(15x^2ln(x)-3x^2+25)/(75)

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

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

y = c_{1} x^{2} + \frac{c _{2}}{x ^{3}} + \frac{15 x ^{2} ln ( x ) - 3 x ^{2} + 25}{75}

Solution steps

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

Solve linear ODE:

y = c_{1} x^{2} + \frac{c _{2}}{x ^{3}} + \frac{15 x ^{2} ln ( x ) - 3 x ^{2} + 25}{75}

y = c_{1} x^{2} + \frac{c _{2}}{x ^{3}} + \frac{15 x ^{2} ln ( x ) - 3 x ^{2} + 25}{75}

What is the solution for x^2y^{''}+2xy^'-6y=x^2-2 ?
The solution for x^2y^{''}+2xy^'-6y=x^2-2 is y=c_{1}x^2+(c_{2})/(x^3)+(15x^2ln(x)-3x^2+25)/(75)