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$The solution of d.E (x^{2} + y^{2} + x) d x - (2 x^{2} + 2 y^{2} - y) d y = 0 is$

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x−2y+lnx2+y2=c

x−2y+lnx2−y2=c

x−2y+lnx2+2y2=c

x−2y+12lnx2+y2=c

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detailed solution

Correct option is D

x2+y2dx−2x2+y2dy+xdx+ydy=0⇒dx−2dy+xdx+ydyx2+y2=0 Integrations both sides x−2y+12ln⁡x2+y2=c

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The solution of d.E x2+y2+xdx−2x2+2y2−ydy=0 is

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$The solution of d.E (x^{2} + y^{2} + x) d x - (2 x^{2} + 2 y^{2} - y) d y = 0 is$