What is the solution for x^2(dy)/(dx)+2xy=ln(x) ?

The solution for x^2(dy)/(dx)+2xy=ln(x) is y=(ln(x))/x-1/x+(c_{1})/(x^2)

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x^2(dy)/(dx)+2xy=ln(x)

x^{2} \frac{d y}{d x} + 2 x y = ln (x)

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

Solution steps

x^{2} \frac{d y}{d x} + 2 x y = ln (x)

Solve linear ODE:

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

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

\int \frac{3 x}{x ^{2} - 2} d x

\int (5 x^{2} + 3 x^{- 2}) d x

\frac{d y}{d x}, (cos (π x) + sin (π y))^{5} = 23

n = 1 \sum \infty r^{n}

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