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

The solution for x^2y^{''}+xy^'-y=sqrt(x) is y=c_{1}x+(c_{2})/x-sqrt(x)-(x^{1/2})/3

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

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

y = c_{1} x + \frac{c _{2}}{x} - x - \frac{x ^{\frac{1}{2}}}{3}

Solution steps

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

Solve linear ODE:

y = c_{1} x + \frac{c _{2}}{x} - x - \frac{x ^{\frac{1}{2}}}{3}

y = c_{1} x + \frac{c _{2}}{x} - x - \frac{x ^{\frac{1}{2}}}{3}

x^{2} y^{^{'}} + 3 x y = e^{- x}

\int 2 x^{2} d x

x + \frac{1}{x ^{3}} (1.2)

\frac{\partial}{\partial y} (3 x^{3} y^{2})

\frac{d}{d x} (x (1 - x))

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