(TRICKY) Approximate y(1.1) for the non-linear initial value problem d?y dy 2y = 0, dx y(0) = 1, y (0) = 1 dx2 1 using the improved Euler's method with h = 0.1. The exact solution is y(x) = so y(1.1) = -10. In this case the approximation is badly 1 - x off. How small a step-size do you need to pick to get the relative error under 10%.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.