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

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

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

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

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

Solution steps

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

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