The solution of the differential equation d y d x - y + 3 x log e ( y + 3 x ) + 3 = 0 is (where C is a…

The solution of the differential equation dydx-y+3xloge(y+3x)+3=0 is
(where C is a constant of integration)
  1. x-12loge(y+3x)2=C
  2. x-loge(y+3x)=C
  3. y+3x-12logex2=C
  4. x-2loge(y+3x)=C

Solution

  dydx-y+3xln(y+3x)+3=0
dydx+3=y+3xln(y+3x)
ddx(y+3x)=y+3xln(y+3x)
∫ln(y+3x)(y+3x)d(y+3x)=∫dx
Let ln(y+3x)=t
1(y+3x)d(y+3x)=dt
∫tdt=∫dx
t22=x+c
(ln(y+3x))22=x+c

Asked in: JEE Main 2020 (04 Sep Shift 2)

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