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Let a solution y=y(x) of the differential equation x x^2-1 d y-y y^2-1 d x=0 satisfy y(2)= 2 3 Statement 1 y(x)= ( ⁻¹ x- 6 ) Statement 2 y(x) is given by 1 y = 2 3 x - 1- 1 x^2

Options

  1. AStatement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
  2. BStatement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
  3. CStatement 1 is true, Statement 2 is false.
  4. DStatement 1 is false, Statement 2 is true

Correct answer

C. Statement 1 is true, Statement 2 is false.

Step-by-step solution

d y d x = y y^2-1 x x^2-1 d y y y^2-1 = d x x x^2-1 ⁻¹ y= ⁻¹ x+C At x=2, y= 2 3 6 = 3 +C C=- 6 Now, y= ( ⁻¹ x- 6 ) aligned & = [ ⁻¹ 1 x - ⁻¹ 3 2 ] & = [ ⁻¹ ( 3 2 x + 1- 1 x^2 1- 3 4 ) ] 1 y & = 3 2 x + 1 2 1- 1 x^2

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