A curve satisfies $x\dfrac{\mathrm{d}y}{\mathrm{d}x}=y+\sqrt{xy}$ for $x0$ and $y0$. Given t

Question

A curve satisfies $x\dfrac{\mathrm{d}y}{\mathrm{d}x}=y+\sqrt{xy}$ for $x>0$ and $y>0$. Given that $y(1)=4$, find $y$ in terms of $x$, stating the largest interval on which the solution is positive.

Accepted Answer

$y=\dfrac{x}{4}(\ln x+4)^2,\quad x>\mathrm e^{-4}$

Square-root growth of a solution curve

Square-root growth of a solution curve

Solution:

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