Solve y=sin(e^x^2)

$$y = \sin ( e ^ { x ^ { 2 } } )$$

Solve for x (complex solution)

$$x\in \cup n_{2},\sqrt{\ln(-i\ln(-\sqrt{1-y^{2}}+iy)+2\pi n_{1})+2i\pi n_{2}},-\sqrt{\ln(-i\ln(-\sqrt{1-y^{2}}+iy)+2\pi n_{1})+2i\pi n_{2}}\text{, }n_{1}\in \mathrm{Z}$$

$$x\in \cup n_{4},-\sqrt{\ln(-i\ln(\sqrt{1-y^{2}}+iy)+2\pi n_{3})+2i\pi n_{4}}\text{, }n_{3}\in \mathrm{Z}\text{, }\left(n_{3}\neq 0\text{ or }y\neq 0\right)\text{ and }n_{3}\neq \frac{i\ln(\sqrt{1-y^{2}}+iy)}{2\pi }$$

$$x\in \cup n_{4},\sqrt{\ln(-i\ln(\sqrt{1-y^{2}}+iy)+2\pi n_{3})+2i\pi n_{4}}\text{, }n_{3}\in \mathrm{Z}\text{, }\left(n_{3}\neq 0\text{ or }y\neq 0\right)\text{ and }n_{3}\neq \frac{i\ln(\sqrt{1-y^{2}}+iy)}{2\pi }$$

Solve for x

$$x=-\sqrt{\ln(-\arcsin(y)+2\pi n_{1}+\pi )}\text{, }n_{1}\in \mathrm{Z}\text{, }n_{1}\geq 0$$

$$x=\sqrt{\ln(-\arcsin(y)+2\pi n_{1}+\pi )}\text{, }n_{1}\in \mathrm{Z}\text{, }n_{1}\geq 0$$

$$x=-\sqrt{\ln(\arcsin(y)+2\pi n_{2})}\text{, }n_{2}\in \mathrm{Z}\text{, }\left(y\leq 1\text{ and }n_{2}\geq 1\text{ and }y>0\right)\text{ or }\left(n_{2}\geq 1\text{ and }|y|\leq 1\right)\text{ or }\left(y\leq 1\text{ and }n_{2}\geq 0\text{ and }y\geq \sin(1)\right)$$

$$x=\sqrt{\ln(\arcsin(y)+2\pi n_{2})}\text{, }n_{2}\in \mathrm{Z}\text{, }\left(y\leq 1\text{ and }n_{2}\geq 1\text{ and }y>0\right)\text{ or }\left(n_{2}\geq 1\text{ and }|y|\leq 1\right)\text{ or }\left(y\leq 1\text{ and }n_{2}\geq 0\text{ and }y\geq \sin(1)\right)\text{, }|y|\leq 1$$

Solve for y

$$y=\sin(e^{x^{2}})$$