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Question

dydx=x+y+12x+2y+3

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Solution

Given,

dydx=x+y+12x+2y+3

dydx=x+y+12(x+y)+3

substitute x+y=v1+dydx=dvdx

dvdx1=v+12v+3

dvdx=3v+42v+3

2v+33v+4dv=dx

integrating on both sides, we get,

2v+33v+4dv=dx

23v+19log|3v+4|=x+c

23(x+y)+19log|3(x+y)+4|=x+c

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