What is the solution for y^{''}-1/x y^'+1/(x^2)y= 2/x ?

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

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y^{''}-1/x y^'+1/(x^2)y= 2/x

y^{^{''}} - \frac{1}{x} y^{^{'}} + \frac{1}{x ^{2}} y = \frac{2}{x}

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

Solution steps

y^{''} (x) - \frac{1}{x} y^{'} (x) + \frac{1}{x ^{2}} y = \frac{2}{x}

Solve linear ODE:

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

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

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