If the curve $y=y(x)$ is the solution of the differential equation $2\left({x}^{2}+{x}^{5/4}\right)dy-y\left(x+{x}^{1/4}\right)dx=2{x}^{9/4}dx,x0$ 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 $2\left({x}^{2}+{x}^{5/4}\right)dy-y\left(x+{x}^{1/4}\right)dx=2{x}^{9/4}dx,x>0$ 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)dy-y\left(x+{x}^{1…

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