Question

Let y depends on x. The solution of the following differential equation is dy +[(1 – 2x)eXy2 + 2xy]dx = 0 ye*+ Ce*?y2 = 0 ye*+Coy2-1 1 y=- ex+ Cot? yet + Coty? o

Answer 1

Griven differential equation Pagerd dy + [(1-27) ety? +20y) dx = 0 divide up Rq dy du [(1-24) " ya +2ny) = + 2 dy + 2n4= (2x-1) egy doc 7 (2x-1) e dy 27 + 11 y y z dn Let = v to to du ap T- = dn 이거 -du +2 1.71 = (2x-1) xP 2UX 1) dv dx (1-22) e" It is ebay's differential equatim of the form dv + P(1) u Q(81) dri where Ilf Spalda ہ =e

Va) e-n² Solut-im Vem) - T . E I of 'Q (n) to n Q(M) = ((-22) e her - 2M Plul -2ndn I.FC aka = t. I e Solutim K da to vine- -] (1-2938". ex du (4-22) S(1-2%) e da te Val e zkar - Let 2-x2=t (1-281) dnadt valle put value 772 et 7p7a s of t et at V (m) en op? Xon? tc е. a V(X) = vOnE ka tce le ent cen? ch su option thitd 11 zk2 tua is True e ie