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

The solution for x^2y^{''}+2xy^'-2y=x^2ln(x) is y=c_{1}x+(c_{2})/(x^2)+(x^2(4ln(x)-5))/(16)

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

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

y = c_{1} x + \frac{c _{2}}{x ^{2}} + \frac{x ^{2} ( 4 ln ( x ) - 5 )}{16}

Solution steps

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

Solve linear ODE:

y = c_{1} x + \frac{c _{2}}{x ^{2}} + \frac{x ^{2} ( 4 ln ( x ) - 5 )}{16}

y = c_{1} x + \frac{c _{2}}{x ^{2}} + \frac{x ^{2} ( 4 ln ( x ) - 5 )}{16}

What is the solution for x^2y^{''}+2xy^'-2y=x^2ln(x) ?
The solution for x^2y^{''}+2xy^'-2y=x^2ln(x) is y=c_{1}x+(c_{2})/(x^2)+(x^2(4ln(x)-5))/(16)