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#