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Solution of the differential equation (1 + 3x)dy - (1 - 3y)dx = 0, y(1) = 0 is

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  1. x + y + 3xy = 1
  2. x - y + 3xy = 1
  3. x - y - 3xy = 1
  4. x + y - 3xy = 1

Answer (Detailed Solution Below)

Option 3 : x - y - 3xy = 1
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Detailed Solution

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Calculation:

Given,

(1 + 3x) dy – (1 – 3y) dx = 0

On integration both side-

      ---(A)

Initially, y = 0; x = 1 put in equation (A) we get –

⇒  

Put in equation (A)

⇒ 

⇒ 

⇒ 4 = 1 – 3y + 3x – 9xy

⇒ 3x – 3y - 9xy = 3

⇒ x – y – 3xy = 1

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