If y ( x ) is the solution of the differential equation x + 2 d y d x = x 2 + 4 x - 9 , x ≠ - 2 and y 0 = 0 , then y ( - 4 ) is equal to

Step-by-step solution

x + 2 d y d x = x 2 + 4 x + 4 - 13 d y d x =   x + 2 2 x + 2 -   13 ( x + 2 ) d y =   x + 2 - 13 x + 2 d x y = x 2 2 + 2 x - 13 log e ⁡ x + 2 + C If x = 0 then y = 0 0 =   0 + 0 - 13   l o g 2 + C C   = 13 log ⁡ ( 2 ) If x =   - 4 , then y y = 16 2 - 8 - 13 log ⁡ - 2 + 13 log ⁡ | 2 | y = 0 Hence, answer is 0 .