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If d y d x =2 e^x y^3, y(0)= 1 2 then what is 4 y^2 (2-e^x ) equal to?

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

A. 1

Step-by-step solution

d y d x =2 e^x y^3 d y d x^3 =2 e^x d x Integrating both sides w.r. to x- 1 2 y^2 =2 e^x+c ....(i) aligned y(0) & = 1 2 -2 & =2+c c=-4 aligned The solution is - 1 2 y^2 =2 e^x-4 array ll & 4 y^2 (e^x )-8 y^2=-1 & 4 y^2 (2-e^x )= 1 array

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