Differential EquationHard
Question
If y(x) is the solution of the differential equation (x + 2) dy/dx = x2 + 4x − 9, x ≠ − 2 and y(0) = 0, then y(− 4) is equal to :
Options
A.2
B.0
C.- 1
D.1
Solution
(x + 2)
= (x + 2)2 - 13 
= (x + 2) - 
y =
+ 2x - 13 ln(x + 2) + C at x = 0, y = 0 ⇒ c = 13 ln2
y =
+ 2x - 13 ln|x + 2| + 13 ln2
Now y(-4) = 8 - 8 - 13 ln|-4 + 2| + 13ln2 = 0
= (x + 2)2 - 13 = (x + 2) - y =
+ 2x - 13 ln(x + 2) + C at x = 0, y = 0 ⇒ c = 13 ln2y =
+ 2x - 13 ln|x + 2| + 13 ln2Now y(-4) = 8 - 8 - 13 ln|-4 + 2| + 13ln2 = 0
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