Find the general solution of these first order differential equations (1

aspifsGak5u 2022-01-21 Answered
Find the general solution of these first order differential equations
(1x)y=y2
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Expert Answer

usumbiix
Answered 2022-01-21 Author has 33 answers
Given that:
(1x)y=y2
Consider
(1x)y=y2
(1x)dydx=y2
dyy2=11xdx
Integrate on both sides
1y2dy=11xdx
Let u=1x  dudx=1
du=dx
Hence we have
1y2dy=1udu
[yndn=yn+1n+1+c]
y2+12+1=ln(1x)+c
1y=ln(1x)+c
y=1ln(1x)c
The general solution is
y=1ln(1x)c
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