Question

Solve the given initial-value problem. The DE is homogeneous. xv2 dx = y3 – x3, 7(1) = 4 y=x(64 – In(x))(+)

Answer 1

Given D.E. isi ny dy - y3 w3 dn y 3 x3 dy dn nya Clearly put above DE is Homo. y=va - dy - xt ndy dan We get, SAKA) up k te up zky nk qk-sken Vandv du 12113 vt n dy x3 (v3_1) 35 M2 du 1 » n dy da - V3_1-ve(ve) v2 dy 31- " d게 AP up - v² du = -da ved vt da

by using definition of solution of homogeneous differential eq i was solved this problem

which is in variable separable form. Integrating above eq we get . fredx+ ft dn ac M + enim) - C put v= 4x +3 en (n) = 36. 21342 » y3 = (30-3 enim)) as f3c-3 enca but y(i)=4 a= [32 BC = 64 substitute value of c in ea 7 we get 64-Ben(n) 4 - f (64 – 3.en cm) 252 us (64-3. ewens of which Given is saslu D.E. Iu- 1 1 64- 3 ening