What is the solution for (dy)/(dx)+3/x y=(ln(x))/(x^2) ?

The solution for (dy)/(dx)+3/x y=(ln(x))/(x^2) is y=(ln(x))/(2x)-1/(4x)+(c_{1})/(x^3)

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(dy)/(dx)+3/x y=(ln(x))/(x^2)

\frac{d y}{d x} + \frac{3}{x} y = \frac{ln ( x )}{x ^{2}}

y = \frac{ln ( x )}{2 x} - \frac{1}{4 x} + \frac{c _{1}}{x ^{3}}

Solution steps

\frac{d y}{d x} + \frac{3}{x} y = \frac{ln ( x )}{x ^{2}}

Solve linear ODE:

y = \frac{ln ( x )}{2 x} - \frac{1}{4 x} + \frac{c _{1}}{x ^{3}}

y = \frac{ln ( x )}{2 x} - \frac{1}{4 x} + \frac{c _{1}}{x ^{3}}

\int - \frac{1}{x ^{2} - 1} d x

\int_{1}^{5} t ln (t) d t

y^{^{'}} = sec^{2} (x) (2 + y)^{2}, y (π) = - 5

y^{^{''}} + 4 y = 3 sin (2 x)

What is the solution for (dy)/(dx)+3/x y=(ln(x))/(x^2) ?
The solution for (dy)/(dx)+3/x y=(ln(x))/(x^2) is y=(ln(x))/(2x)-1/(4x)+(c_{1})/(x^3)