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GATE BT 2022 | Question: 37

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Consider the ordinary differential equation $\dfrac{dy}{dx} = f(x,y) = 2x^{2} – y^{2}.$ If $y(1)=1,$ the value(s) of $y(1.5),$ using the Euler’s implicit method $\left[y_{n+1}=y_{n}+hf(x_{n+1},y_{n+1}) \right]$ with a step size of $h=0.5,$ is (are)

  1. $-1-5 \sqrt{0.3}$
  2. $-1+5 \sqrt{0.3}$
  3. $1+5 \sqrt{0.3}$
  4. $1-5 \sqrt{0.3}$

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