Solucionar cos(sqrt{y}x)=0

$$\cos ( \sqrt{ y } x ) = 0$$

Resolver para x (solución compleja)

$$x=2\pi y^{-\frac{1}{2}}n_{1}+\frac{3\pi y^{-\frac{1}{2}}}{2}\text{, }n_{1}\in \mathrm{Z}$$

$$x=2\pi y^{-\frac{1}{2}}n_{2}+\frac{\pi y^{-\frac{1}{2}}}{2}\text{, }n_{2}\in \mathrm{Z}\text{, }y\neq 0$$

Resolver para y (solución compleja)

$$y=\frac{\left(\frac{\pi \left(4n_{1}+1\right)}{x}\right)^{2}}{4}\text{, }n_{1}\in \mathrm{Z}\text{, }arg(\frac{2\pi n_{1}}{x}+\frac{\pi }{2x})<\pi$$

$$y=\frac{\left(\frac{\pi \left(4n_{2}+3\right)}{x}\right)^{2}}{4}\text{, }n_{2}\in \mathrm{Z}\text{, }arg(\frac{2\pi n_{2}}{x}+\frac{3\pi }{2x})<\pi \text{, }x\neq 0$$

Resolver para x

$$x=\frac{\pi n_{1}}{\sqrt{y}}+\frac{\pi }{2\sqrt{y}}$$

$$n_{1}\in \mathrm{Z}$$

$$y>0$$

Resolver para y

$$y=\frac{\left(\frac{\pi \left(2n_{1}+1\right)}{x}\right)^{2}}{4}$$

$$n_{1}\in \mathrm{Z}$$

$$\left(n_{1}<0\text{ and }x<0\right)\text{ or }\left(n_{1}>-1\text{ and }x>0\right)$$