The solution curve of the differential equation ((y2x2+18)2−164)dydx=x2+2y2x passes through the point (2,3), the curve is given by

(y4x4+2y28x2)dydx=x2+4y22x y2(4y2+x2)4x4dydx=x2+4y22x simplify and get y2dy=2x3

The solution curve of the differential equation ((y2x2+18)2−164)dydx=x2+2y2x passes through the point (2,3), the curve is given by

(y4x4+2y28x2)dydx=x2+4y22x y2(4y2+x2)4x4dydx=x2+4y22x simplify and get y2dy=2x3

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The solution curve of the differential equation $({(\frac{y^{2}}{x^{2}} + \frac{1}{8})}^{2} - \frac{1}{64}) \frac{d y}{d x} = \frac{x}{2} + \frac{2 y^{2}}{x}$ passes through the point (2,3), the curve is given by

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$2 x^{4} - 2 y^{3} - 5 = 0$

$3 x^{4} - 2 y^{3} + 6 = 0$

$x^{4} + y^{3} = 43$

$3 {(x - 2)}^{4} - 2 {(y - 3)}^{3} = 0$

answer is B.

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Detailed Solution

$(\frac{y^{4}}{x^{4}} + \frac{2 y^{2}}{8 x^{2}}) \frac{d y}{d x} = \frac{x^{2} + 4 y^{2}}{2 x}$

$(\frac{y^{2} (4 y^{2} + x^{2})}{4 x^{4}}) \frac{d y}{d x} = \frac{x^{2} + 4 y^{2}}{2 x}$

simplify and get $y^{2} d y = 2 x^{3}$

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The solution curve of the differential equation ((y2x2+18)2−164)dydx=x2+2y2x passes through the point (2,3), the curve is given by

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The solution curve of the differential equation $({(\frac{y^{2}}{x^{2}} + \frac{1}{8})}^{2} - \frac{1}{64}) \frac{d y}{d x} = \frac{x}{2} + \frac{2 y^{2}}{x}$ passes through the point (2,3), the curve is given by