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Euler's method practice problems

Step along the slope field: yₙ₊₁ = yₙ + h·f(tₙ, yₙ). 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.

Use Euler's method with step size \( \displaystyle h = \frac{1}{2} \) to approximate \( \displaystyle y(1) \) for \( \displaystyle y' = t^{2} + y \), \( \displaystyle y(0) = 3 \).

Problem 6.211medium✓ Nihil obstat

Use Euler's method with step size \( \displaystyle h = \frac{1}{2} \) to approximate \( \displaystyle y(2) \) for \( \displaystyle y' = t y \), \( \displaystyle y(0) = 1 \).

Problem 6.212medium✓ Nihil obstat

Use Euler's method with step size \( \displaystyle h = \frac{1}{4} \) to approximate \( \displaystyle y(\frac{3}{2}) \) for \( \displaystyle y' = 1 - y \), \( \displaystyle y(1) = 3 \).

Problem 6.213medium✓ Nihil obstat

Use Euler's method with step size \( \displaystyle h = \frac{1}{10} \) to approximate \( \displaystyle y(\frac{3}{10}) \) for \( \displaystyle y' = t + y \), \( \displaystyle y(0) = 3 \).

Problem 6.214medium✓ Nihil obstat

Use Euler's method with step size \( \displaystyle h = \frac{1}{2} \) to approximate \( \displaystyle y(\frac{5}{2}) \) for \( \displaystyle y' = 2 t + y \), \( \displaystyle y(1) = 2 \).

Problem 6.215medium✓ Every equation proved

Use Euler's method with step size \( \displaystyle h = \frac{1}{10} \) to approximate \( \displaystyle y(\frac{1}{5}) \) for \( \displaystyle y' = t^{2} + y \), \( \displaystyle y(0) = 2 \).

Problem 6.216medium✓ Nihil obstat

Use Euler's method with step size \( \displaystyle h = \frac{1}{10} \) to approximate \( \displaystyle y(\frac{3}{10}) \) for \( \displaystyle y' = - t^{2} + y \), \( \displaystyle y(0) = 3 \).

Problem 6.217medium✓ Nihil obstat

Use Euler's method with step size \( \displaystyle h = \frac{1}{10} \) to approximate \( \displaystyle y(\frac{3}{10}) \) for \( \displaystyle y' = 2 y \), \( \displaystyle y(0) = 2 \).

Problem 6.218medium✓ Nihil obstat

Use Euler's method with step size \( \displaystyle h = \frac{1}{5} \) to approximate \( \displaystyle y(\frac{4}{5}) \) for \( \displaystyle y' = t - y \), \( \displaystyle y(0) = 2 \).

Problem 6.219medium✓ Nihil obstat

Use Euler's method with step size \( \displaystyle h = \frac{1}{5} \) to approximate \( \displaystyle y(\frac{8}{5}) \) for \( \displaystyle y' = t^{2} + y \), \( \displaystyle y(1) = 3 \).

Problem 6.220medium✓ Nihil obstat