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Question

If $y=y(x)$ is the solution curve of the differential equation $\left(x^2-4\right) \mathrm{d} y-\left(y^2-3 y\right) \mathrm{d} x=0, x>2, y(4)=\frac{3}{2}$ and the slope of the curve is never zero, then the value of $y(10)$ equals :

$\frac{3}{1+(8)^{1 / 4}}$
$\frac{3}{1-(8)^{1 / 4}}$
$\frac{3}{1-2 \sqrt{2}}$
$\frac{3}{1+2 \sqrt{2}}$

Solution

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