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Question

Solution of the different equation, $$ydx - xdy + x{y^2}dx = 0$$ can be.


A
2x+x2y=λy
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B
2y+y2x=λy
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C
2yy2x=λy
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D
none of these
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Solution

The correct option is A $$2x + {x^2}y = \lambda y$$
$$\cfrac{ydx-xdy}{y^2} = d(\cfrac{x}{y})$$
Hence, 
$$\cfrac{ydx-xdy}{y^2} + xdx = 0$$
$$d(\cfrac{x}{y}) + xdx = 0$$
Integrating both sides we get,
$$\cfrac{x}{y} + \cfrac{x^2}{2} = C$$
$$2x+x^2 y  = \lambda y$$

Mathematics

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