What is the solution for y^'=-(2x)/((1+x^2))y+1/(x(1+x^2)) ?

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

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y^'=-(2x)/((1+x^2))y+1/(x(1+x^2))

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

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

Solution steps

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

Solve linear ODE:

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

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

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