The equation of the curve satisfying the differential equation $$y2x2+1=2xdydx$$ passing through the point (1$$,$$1) is

Correct option is 3y=45−x2−2lnx

Questions

The equation of the curve satisfying the differential equation $y^{2} (x^{2} + 1) = 2 x \frac{d y}{d x}$ passing through the point (1,1) is

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y=45+x+lnx

y=45−x+2lnx

y=45−x2−2lnx

y=45−x2+2lnx

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detailed solution

Correct option is C

Given differential equation after rearranging the terms is∫x2+12xdx=∫dyy212∫x dx+∫1xdx=∫dyy2⇒12x22+ln⁡x=−1y+C∵ It passes through (1,1)⇒14=−1+C⇒C=54⇒1y=54−x2+2ln⁡x4⇒y=45−x2−2ln⁡x

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The equation of the curve satisfying the differential equation y2x2+1=2xdydx passing through the point (1,1) is

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The equation of the curve satisfying the differential equation $y^{2} (x^{2} + 1) = 2 x \frac{d y}{d x}$ passing through the point (1,1) is