Dar solución a las siguientes ecuaciones diferenciales de primer orden empleando el método de variables separables?

Respuesta : <img src="https://tex.z-dn.net/?f=3e%5E%7Bx%7D%2A%5Ctan%28y%29dx%2B%282-e%5E%7Bx%7D%29%2A%5Csec%5E%7B2%7D%28y%29dy%3D0%5C%5C3e%5E%7Bx%7D%2A%5Ctan%28y%29dx%3D-%282-e%5E%7Bx%7D%29%2A%5Csec%5E%7B2%7D%28y%29dy" />Multiplicar por - (2 - e ^ x) y por tan(y) a lado y lado : <img src="https://tex.z-dn.net/?f=%5Cdfrac%7B3e%5E%7Bx%7D%7D%7B-%282-e%5E%7Bx%7D%29%7Ddx%3D%5Cdfrac%7B%5Csec%5E%7B2%7D%28y%29%7D%7B%5Ctan%28y%29%7Ddy%5C%5C%5Cdfrac%7B3e%5E%7Bx%7D%7D%7Be%5E%7Bx%7D-2%7Ddx%3D%5Cdfrac%7B%5Csec%5E%7B2%7D%28y%29%7D%7B%5Ctan%28y%29%7Ddy%5C%5C%5Cdfrac%7B%5Csec%5E%7B2%7D%28y%29%7D%7B%5Ctan%28y%29%7Ddy%3D%5Cdfrac%7B3e%5E%7Bx%7D%7D%7Be%5E%7Bx%7D-2%7Ddx" />Ya están separadas las variables, ahora se procede a integrar : <img src="https://tex.z-dn.net/?f=%5Cint%20%5Cdfrac%7B%5Csec%5E%7B2%7D%28y%29%7D%7B%5Ctan%28y%29%7Ddy%7D%20%3D%5Cint%20%5Cdfrac%7B3e%5E%7Bx%7D%7D%7Be%5E%7Bx%7D-2%7Ddx" />Usar las sustituciones : <img src="https://tex.z-dn.net/?f=u%3D%5Ctan%28y%29%5C%5Cdu%3D%5Csec%5E%7B2%7D%28y%29dy%5C%5C%5C%5Cv%3De%5E%7Bx%7D-2%5C%5Cdv%3De%5E%7Bx%7Ddx" /><img src="https://tex.z-dn.net/?f=%5Cint%20%5Cfrac%7Bdu%7D%7Bu%7D%3D3%20%5Cint%20%5Cfrac%7Bdv%7D%7Bv%7D%5C%5C%20%5Cln%7Cu%7C%3D3%2A%5Cln%7Cv%7C%2BC%5C%5C%5Cln%28%5Ctan%28y%29%29%3D3%2A%5Cln%28e%5E%7Bx%7D-2%29%2BC%5C%5Ce%5E%7B%5Cln%28%5Ctan%28y%29%29%7D%3D%20e%5E%7B3%2A%5Cln%28e%5E%7Bx%7D-2%29%2BC%7D" />.