What is the solution for x((dy)/(dx))+3y= 1/x ?

The solution for x((dy)/(dx))+3y= 1/x is y= 1/(2x)+(c_{1})/(x^3)

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x((dy)/(dx))+3y= 1/x

x (\frac{d y}{d x}) + 3 y = \frac{1}{x}

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

Solution steps

x (\frac{d y}{d x}) + 3 y = \frac{1}{x}

Solve linear ODE:

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

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

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\frac{d y}{d x}, 25 x = y^{4}

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What is the solution for x((dy)/(dx))+3y= 1/x ?
The solution for x((dy)/(dx))+3y= 1/x is y= 1/(2x)+(c_{1})/(x^3)