Question: Use i) Euler's Method and ii) the Midpoint Method to determine the given value of (y) for the following problems: a. (frac{d y}{d x}=2 y,
Use i) Euler's Method and ii) the Midpoint Method to determine the given value of \(y\) for the following problems:
a. \(\frac{d y}{d x}=2 y, y(0)=2\). Find \(y(1)\) with \(h=0.1\).
b. \(\frac{d y}{d x}=x-y, y(0)=1\). Find \(y(2)\) with \(h=0.2\).
c. \(\frac{d y}{d x}=x \sqrt{1-y^{2}}, y(1)=0\). Find \(y(2)\) with \(h=0.2\).
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