Question Number 104845 by john santu last updated on 24/Jul/20

solve y′ = y−x−1+(x−y+2)^(−1)

Answered by john santu last updated on 24/Jul/20

(dy/dx) = −(x−y+2)+1+(x−y+2)^(−1)   set x−y+2 = m   (dm/dx) = 1−(dy/dx) ⇒ (dy/dx) = 1−(dm/dx)  ⇔ 1−(dm/dx) = −m+1+m^(−1)   (dm/dx) = ((m^2 −1)/m) ⇒ ((m.dm)/(m^2 −1)) = dx  ∫( (m/(m^2 −1)))dm = ∫ dx   ∫ ((d(m^2 −1))/(m^2 −1)) = 2x + c  ln (m^2 −1) = 2x + c  m^2  = Ce^(2x)  + 1   ⇒(x−y+2)^2  = Ce^(2x)  + 1