If y   ( x ) is the solution of the differential equation x + 2 d y d x = x 2 + 4 x - 9 ,    …

If y (x) is the solution of the differential equation x+2dydx=x2+4x-9,  x ≠ -2  and y0=0, then y(-4) is equal to 
  1. -1
  2. 1
  3. 0
  4. 2

Solution

x+2dydx=x2+4x+4-13

dydx= x+22x+2- 13(x+2)

dy= x+2-13x+2dx

y=x22+2x-13loge⁡x+2+C

If x=0 then y=0

0= 0+0-13 log2+C

C =13log⁡(2)

If x= -4, then y

y=162-8-13log⁡-2+13log⁡|2|

y=0

Hence, answer is 0.

Asked in: JEE Main 2015 (10 Apr Online)

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