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$The solution of e^{\frac{x (y^{2} - 1)}{y}} \{x y^{2} d y + y^{3} d x\} + {y d x - x d y} = 0 is$

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exy+exy+c=0

exy−exy+c=0

exy+eyx+c=0

exy−eyx+c=0

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detailed solution

Correct option is A

exy2−1yy2(xdy+ydx)+(ydx−xdy)=0exyy2(xdy+ydx)+exy(ydx−xdy)=0exy(xdy+ydx)+exydxy=0⇒exy+exy+c=0

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The solution of exy2−1yxy2dy+y3dx+{ydx−xdy}=0 is

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$The solution of e^{\frac{x (y^{2} - 1)}{y}} \{x y^{2} d y + y^{3} d x\} + {y d x - x d y} = 0 is$