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GATE 2024 MT – Question 37

Engineering Mathematics · Differential equations · 2 marks · Multiple choice

If $dy/dx=4xy$ and $y(0)=1$, then

  1. $y=2x^2+1$
  2. $y=2e^{2x^2}-1$
  3. $y=2e^{x^2}-1$
  4. $y=e^{2x^2}$

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Show answer and explanation

Correct answer: (D) $y=e^{2x^2}$

Explanation

Separate variables: dy/y=4x dx, so ln y=2x²+C.

The initial condition gives C=0.

Thus **y=exp(2x²), D**; differentiating verifies y′=4xy.