PROBLEM 4 [Solving Ordinary Differential Equations] Solve the following ODE: \(\frac{d y}{d x}=1+\frac{x}{y} \quad y(1)=1\)a) Using Euler's method, for 1≤x≤4 and a step of 0.5 b) Using Euler's method, for 1≤x≤4 and a step of 0.25. c) Estimate your error in x-4 using the Richardson formula and provide an answer with the correct number of significant digits for y(4).

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PROBLEM 4 [Solving Ordinary Differential Equations]

Solve the following ODE:

\(\frac{d y}{d x}=1+\frac{x}{y} \quad y(1)=1\)

a) Using Euler's method, for 1≤x≤4 and a step of 0.5

b) Using Euler's method, for 1≤x≤4 and a step of 0.25.

c) Estimate your error in x-4 using the Richardson formula and provide an answer with the correct number of significant digits for y(4).

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milcah answered 2 years ago

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