would anyone be able to show us how you would find the general solution of this differential equation in implicit form for
$\displaystyle \frac{\mathrm{d} y}{\mathrm{d} x}=\frac{2y^{1/2}(2e^{2x}-5)}{3(e^{2x}-5x)^{2/3}}$ $\displaystyle (y>0)$
would anyone be able to show us how you would find the general solution of this differential equation in implicit form for
$\displaystyle \frac{\mathrm{d} y}{\mathrm{d} x}=\frac{2y^{1/2}(2e^{2x}-5)}{3(e^{2x}-5x)^{2/3}}$ $\displaystyle (y>0)$
Pretty close to trivial, isn't it? That's clearly a separable equation:
$\displaystyle y^{-1/2}dy= \frac{2}{3}\frac{\left(e^{2x}- 5x\right)^{-2/3}}{2e^{2x}- 5}dx$
Integrate. (Do you recognize that $\displaystyle (e^{2x}- 5x)'= 2e^{2x}- 5$?)