How to you find the general solution of $dy/dx=x/(1+x^2)$ ?

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Answer 1 · 2017-05-10T19:12:49

Multiply both sides by $dx$ and then integrate.

Given: $dy/dx=x/(1+x^2)$

Multiply both sides by $dx$

$dy=x/(1+x^2)dx$

Integrate:

$intdy=intx/(1+x^2)dx$

$intdy=1/2int(2x)/(1+x^2)dx$

$intdy = 1/2(du)/u$

$y = 1/2ln(u)+ C$

$y = 1/2ln(x^2+1)+C$

$y = ln(sqrt(x^2+1))+C$

How to you find the general solution of dy/dx=x/(1+x^2)dy/dx=x/(1+x^2)?