Solve: ( 1 + ex/y )dx + ex/y ( 1 - x/y) dy = 0 The answer given in the book is : x + y ex/y = C1 Share with your friends Share 13 Manbar Singh answered this The given differential equation is,1+ex/y dx + ex/y1-xy dy = 0⇒dxdy = ex/yxy-11+ex/y ............1put x = vy⇒dxdy = v + ydvdyv + ydvdy = evv-11+ev⇒ ydvdy = vev - ev1 + ev - v⇒ydvdy = vev - ev - v - vev1 + ev⇒ydvdy = -v+ev1+ev⇒1 + evv+ev dv = -dyyIntegrating both sides, we get∫1 + evv+ev dv = -∫dyy ........2Let I = ∫1 + evv+ev dv Put v+ ev = t1 + ev dv = dtso, I = ∫dtt = log t = logv+evSo, from 2, we get logv+ev = - log y + log C⇒logxy + ex/y + log y = log C⇒log yxy + ex/y = log C⇒yxy + ex/y = C⇒x + y ex/y = C 46 View Full Answer
