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Question

The soultion of y5x+yxdydx=0 is-

A
x44+15(xy)5=C
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B
x55+14(xy)4=C
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C
(xy)5+x44=C
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D
(xy)4+x55=C
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Solution

The correct option is B x55+14(xy)4=C
Given,
y5x+yxdydx=0

Divide above equation by y5x

dyy5dx+1+1y4x=0 (1)

let 1y4=t
4y5dydx=dtdx

(1)dt4dx+tx=1

dtdx+4tx=4

P=4x,q=4

I.f.=eP.dx

=e4xdx

=elogx4
=x4

Complete solution is
t×x4=x4×4dx

t×x4=4x55+c

x4y4=4x45+c
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