# Trying to solve this seemingly simple first order non-linear differential equation: y

Trying to solve this seemingly simple first order non-linear differential equation:
${y}^{\prime }+{y}^{2}=\mathrm{cos}2x$
Considered separation of variables and bernoulli methods but figured it's not applicable. Please I need a hint.
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Ronnie Glenn
${y}^{\prime }+{y}^{2}=\mathrm{cos}\left(2x\right)$
Change of function: $y=\frac{{Y}^{\prime }}{Y}\phantom{\rule{1em}{0ex}}\to \phantom{\rule{1em}{0ex}}{y}^{\prime }=\frac{{Y}^{″}}{Y}-\frac{{Y}^{\prime 2}}{{Y}^{2}}$
$\frac{{Y}^{″}}{Y}=\mathrm{cos}\left(2x\right)$
The general solution involves the Mathieu functions:
$Y={c}_{1}\text{MathieuC}\left(0,\frac{1}{2},x\right)+{c}_{2}\text{MatieuS}\left(0,\frac{1}{2},x\right)$
$y\left(x\right)=\frac{{c}_{1}\frac{d}{dx}\text{MatieuC}\left(0,\frac{1}{2},x\right)+{c}_{2}\frac{d}{dx}\text{MatieuS}\left(0,\frac{1}{2},x\right)}{{c}_{1}\text{MatieuC}\left(0,\frac{1}{2},x\right)+{c}_{2}\text{MatieuS}\left(0,\frac{1}{2},x\right)}$