for the following question:(adsbygoogle = window.adsbygoogle || []).push({});

y`=1/(6e^y-2x)

my problem:

dx-(6e^y-2x)dy=0

so (1/F)(dF/dx)=2

=>F=e^2x

so e^2x-(e^2x)(6e^y-2x)dy=0

so (integration)(d^2x)dx=(1/2)e^2x +h(y)

=>h(y)= -6e^(2x+y)+xye^2x+c

so (1/2)e^2x-6e^(2x+y)+xye^2x+c-0

however the correct answer should be

y=ce^(-2y)+2e^y

does anybody know where my calculations went wrong?

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