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$The general solution of the differential equation y (5 x^{4} y + 1) dx + (x + 2 y + 2 x^{5} y) dy = 0 i s$

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xy2+x5+y2=c

xy+x5y2+y2=c

xy+x5y2+y=c

xy+x5y+y2=c

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detailed solution

Correct option is B

xdy+ydx+5x4y2dx+2x5ydy+2ydy=0→d(xy)+dx5y2+dy2=0 Integrating →xy+x5y2+y2=c

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The general solution of the differential equation y5x4y+1dx+x+2y+2x5ydy=0is

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$The general solution of the differential equation y (5 x^{4} y + 1) dx + (x + 2 y + 2 x^{5} y) dy = 0 i s$