If the curve $y=y(x)$ is the solution of the differential equation $2\left(x^2+x^{5 / 4}\right) d y-y\left(x+x^{1 / 4}\right) d x=2 x^{9 / 4} d x, x0$ which passes through the point $\left(1,1-\frac{4}{3} \log _e 2\right)$, then the value of $y(16)$ is equal to: [JEE Main 2021, 17 Mar (Shift 2)]

Question

If the curve $y=y(x)$ is the solution of the differential equation $2\left(x^2+x^{5 / 4}\right) d y-y\left(x+x^{1 / 4}\right) d x=2 x^{9 / 4} d x, x>0$ which passes through the point $\left(1,1-\frac{4}{3} \log _e 2\right)$, then the value of $y(16)$ is equal to: [JEE Main 2021, 17 Mar (Shift 2)]

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If the curve \(y=y(x)\) is the solution of the differential equation \(2\left(x^2+x^{5 / 4}\right) d y-y\left(x+x^{1 / 4…

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