Solution of the differential equation $$dydx=2x$$−$$y+1x+y+2$$ is

Correct option is 4xy+y22+2y=x2+x+C

Questions

$Solution of the differential equation \frac{d y}{d x} = \frac{2 x - y + 1}{x + y + 2} is$

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xy−y2=2y+C

xy+y2+2y=3x2+C

xy+y2=2y+3x2+C

xy+y22+2y=x2+x+C

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detailed solution

Correct option is D

Given that dydx=2x−y+1x+y+2⇒(x+y+2)dy=(2x−y+1)dx⇒xdy+(y+2)dy=2xdx−ydx+dx⇒xdy+ydx+(y+2)dy=2xdx+dx⇒d(xy)+(y+2)dy=2xdx+dxIntegrating on both sides⇒xy+y22+2y=x2+x+C Therefore, the correct answer is (4).

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Solution of the differential equation dydx=2x−y+1x+y+2 is

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$Solution of the differential equation \frac{d y}{d x} = \frac{2 x - y + 1}{x + y + 2} is$