If $y=y(x)$ is the solution curve of the differential equation $\left(x^2-4\right) d y-\left(y^2-3 y\right) d x=0, x2, y(4)=\frac{3}{2}$ and the slope of the curve is never zero, then the value of $y(10)$ equals : [JEE Main 2024, 27 Jan (Shift 2)]

Question

If $y=y(x)$ is the solution curve of the differential equation $\left(x^2-4\right) d y-\left(y^2-3 y\right) d x=0, x>2, y(4)=\frac{3}{2}$ and the slope of the curve is never zero, then the value of $y(10)$ equals : [JEE Main 2024, 27 Jan (Shift 2)]

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If \(y=y(x)\) is the solution curve of the differential equation \(\left(x^2-4\right) d y-\left(y^2-3 y\right) d x=0, x&…

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