What is the solution for x^2y^{''}+4xy^'+2y= 1/x ?

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

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x^2y^{''}+4xy^'+2y= 1/x

x^{2} y^{^{''}} + 4 x y^{^{'}} + 2 y = \frac{1}{x}

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

Solution steps

x^{2} y^{''} (x) + 4 x y^{'} (x) + 2 y = \frac{1}{x}

Solve linear ODE:

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

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

3 \frac{d y}{d x} + \frac{8}{x y ^{2}} = 0

\frac{d}{d x} (\frac{2}{x + 5})

x \to 0 + lim (cot (x) - csc (x))

\int sec (y) tan (y) d y

\frac{d}{d x} (\frac{1}{x + 7})

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