Al Resolver la ecuación diferencial dy / sen(x - y + 1) = dx ; si y(0) = π - 1, el valor de la constante c corresponde a :1?

Sea<img src="https://tex.z-dn.net/?f=x-y%3Du-1" /> y<img src="https://tex.z-dn.net/?f=x%2By%3Dv%2B1" /> entonces <img src="https://tex.z-dn.net/?f=x%3D%5Cdfrac%7Bu%2Bv%7D%7B2%7D" /> y <img src="https://tex.z-dn.net/?f=y%3D%5Cdfrac%7Bv-u%2B2%7D%7B2%7D" />

Así la ecuación se transforma en <img src="https://tex.z-dn.net/?f=%5Cdfrac%7Bd%5Cleft%28%5Cfrac%7Bv-u%2B2%7D%7B2%7D%5Cright%29%7D%7B%5Csin%20u%7D%3Dd%5Cleft%28%5Cdfrac%7Bu%2Bv%7D%7B2%7D%5Cright%29%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctext%7BDesarrollando%7D%5C%5C%20%5C%5C%20%5C%5C%0A%5Cdfrac%7Bdv-du%7D%7B%5Csin%20u%7D%3Ddu%2Bdv%5C%5C%20%5C%5C%20%5C%5C%0Adv-du%3D%28du%2Bdv%29%5Csin%20u%5C%5C%20%5C%5C%20%5C%5C%0A%281-%5Csin%20u%20%29%5C%2Cdv%3D%281%2B%5Csin%20u%29%5C%2C%20du%5C%5C%20%5C%5C%20%5C%5C%0Adv%3D%5Cdfrac%7B1%2B%5Csin%20u%7D%7B1-%5Csin%20u%7D%5C%2C%20du%5C%5C%20%5C%5C%20%5C%5C%0A%5Cdisplaystyle%0Av%3D%5Cint%20%5Cdfrac%7B1%2B%5Csin%20u%7D%7B1-%5Csin%20u%7D%5C%2C%20du%20%5C%5C%20%5C%5C%20%5C%5C%0Av%3D2%5Ctan%5Cleft%28%5Cdfrac%7Bu%7D%7B2%7D%2B%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cright%29-u%2BC%20%5C%5C%20%5C%5C%20%5C%5C" />

<img src="https://tex.z-dn.net/?f=x%2By-1%3D2%5Ctan%5Cleft%28%5Cdfrac%7Bx-y%2B1%7D%7B2%7D%2B%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cright%29-x%2By-1%2BC%20%5C%5C%20%5C%5C%20%5C%5C%0Ax%3D%5Ctan%5Cleft%28%5Cdfrac%7Bx-y%2B1%7D%7B2%7D%2B%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cright%29%2BC%27%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctext%7BReemplazando%20valores%3A%7D%5C%5C%20%5C%5C%0A0%3D%5Ctan%5Cleft%28%5Cdfrac%7B0-%5Cpi%2B1%2B1%7D%7B2%7D%2B%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cright%29%2BC%27%5C%5C%20%5C%5C%20%5C%5C%0A0%3D%5Ctan%5Cleft%28%5Cdfrac%7B4-%5Cpi%7D%7B4%7D%5Cright%29%2BC%27%5C%5C%20%5C%5C%20%5C%5C%0AC%27%3D%5Ctan%5Cleft%28%5Cdfrac%7B%5Cpi-4%7D%7B4%7D%5Cright%29%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctext%7BSoluci%5C%27on%20de%20la%20EDO%7D%5C%5C%20%5C%5C%20%5C%5C%0Ax%3D%5Ctan%5Cleft%28%5Cdfrac%7Bx-y%2B1%7D%7B2%7D%2B%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cright%29%2B%5Ctan%5Cleft%28%5Cdfrac%7B%5Cpi-4%7D%7B4%7D%5Cright%29" />.