Question
Asked Jun 10, 2019
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Determine a region of the ty-plane for which the given differential equation would have a unique solution whose graph passes through a point (x0, y0) in the region:

(x2+y2)y'=y2

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Expert Answer

Step 1
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The given differential equation is (2+y2)y =. Rewrite the given equation as follows ر-)هر,.م dy (x+y) dx Note that, the function defined for all values ofx andy except the points x 0 and y 0 Therefore, the domain ofthe given function is set of all real numbers except the origin

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Step 2
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Differen x+ y2) with respect to y as follows. iate d (y2 dy d d dy vu -uv (x+y) (xy(2y)-y°(2y) (x+ y _(2y) (x* + y? =y?) (x+y) 2y(x*) (xyy 2x2y 2+y Thus, the differentiation ofthe given function is continuous at all points except the origin

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