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NDA 1 2024 Maths, question 76

Topic: Differential equations

Q76

If dydx=2exy3\frac{dy}{dx}=2e^{x}y^{3}, y(0)=12y(0)=\frac{1}{2} then what is 4y2(2−ex)4y^{2}(2-e^{x}) equal to ?

  1. (a) 11Correct answer
  2. (b) 22
  3. (c) 33
  4. (d) 44

Solution.

Answer: (a) 11

  1. Separate variables: y^(−3)dy = 2e^x dx.
  2. Integration gives −1/(2y²) = 2e^x + C.
  3. With y(0) = 1/2, C = −4.
  4. Rearranging yields 4y²(2 − e^x) = 1 on the solution interval.