Differential EquationHard
Question
A curve y = f(x) passing through (1, 1) given by the solution of the differential equation x2ey. 
- 2xey + tan-1x, is -
- 2xey + tan-1x, is - Options
A.y = log
B.y = log(2x - 1) + (x - 1) tan-1x + 1
C.y = log
D.y = log
Solution
x2ey. 
- 2xey + tan-1x
⇒ x2ey. dy + 2xey =
dx
⇒ d(x2ey) = d(x.tan-1x)
⇒ x2ey = xtan-1x + C
at (1, 1), e =
+ C ⇒ C = e - 0
x2ey = x tan-1 + e -
ey =
y = log
- 2xey + tan-1x⇒ x2ey. dy + 2xey =
dx⇒ d(x2ey) = d(x.tan-1x)
⇒ x2ey = xtan-1x + C
at (1, 1), e =
+ C ⇒ C = e - 0x2ey = x tan-1 + e -
ey =
y = log
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