Question #1918f

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Answer 1 · 2018-02-12T13:33:16

The general solution is:

#y=clnx#

and the particular solution is:

#y = lnx#

The equation is separable:

#dy/dx lnx -y/x = 0#

#dy/dx = 1/lnx y/x#

#dy/y = dx/(xlnx)#

#int dy/y = int dx/(xlnx)#

#ln abs y = int (d(lnx))/lnx#

#ln abs y = ln abs ln x + C#

#y(x) = clnx#

We can find the particular solution determining #c# from the equation:

#y(e) = 1#

#clne = 1#

#c = 1#