how can you prove that (xy+1)dx+x•(x+4y2dy=0

Where you will have an answe x+ lnx+2y^2 -2y=c
in Calculus Answers by Level 12 User (101k points)

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10 Answers

By differentiation of:
by Level 12 User (101k points)
Xy+ lnx+2y^2-2y=c
by Level 12 User (101k points)
We have :
by Level 12 User (101k points)
xdy+ydx+dx/x+4ydy-2dy=0
by Level 12 User (101k points)
x^2 dy+(xy) dx+dx+(4xy-2x) dy=0
by Level 12 User (101k points)
(xy+1) dx+x(x+4y-2) dy=0
by Level 12 User (101k points)
Qed ,
by Level 12 User (101k points)
Note: the integrating factor -
by Level 12 User (101k points)
If we solve the given- is
by Level 12 User (101k points)
F= 1/x
by Level 12 User (101k points)

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