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})/x+xln(x)-x/2

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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 + \frac{c _{2}}{x} + x ln (x) - \frac{x}{2}

Solution steps

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

Solve linear ODE:

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

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

y = \frac{e ^{x} + e ^{- x}}{2}

f (x) = e^{1 - x}

\int x^{2} arctan (7 x) d x

\int \frac{1}{1 - 4 x ^{2}} d x

\frac{d}{d r} (\frac{( r ^{2} - 1 ) ^{3}}{( 2 r + 1 ) ^{5}})

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})/x+xln(x)-x/2