How do you solve the differential \(\displaystyle{y}'{x}{\ln{{\left({x}\right)}}}={y}\)?

Tyson Mcneil

Tyson Mcneil

Answered question

2022-04-11

How do you solve the differential yxln(x)=y?

Answer & Explanation

izvozna39g0

izvozna39g0

Beginner2022-04-12Added 9 answers

Explanation:
To make ln x real, x > 0.
Separating variables and integrating,
1ydy=xlnxdx. So
lny
=lnxd(x22)
=12x2lnx12x2d(lnx)
=12x2lnx12x2xdx
=12x2lnx12x2xdx
=12x2lnxx24+A
So,
y=eAe14x2(2lnx1)
=Ce14x2(2lnx1), where C>0. and so is y.

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