Advanced Engineering Mathematics, 7th Edition

6 Chapter in Review Answers to selected odd-numbered problems begin on page ANS-15.

In Problems 1– 4, construct a table comparing the indicated values of y(x) using Euler’s method, the improved Euler’s method, and the RK4 method. Compute to four rounded decimal places. Use h = 0.1 and then use h = 0.05.

1. y′ = 2 ln xy,     y(1) = 2;y(1.1), y(1.2), y(1.3), y(1.4), y(1.5)
2. y′ = sin x² + cos y²,     y(0) = 0;y(0.1), y(0.2), y(0.3), y(0.4), y(0.5)
3. y′ = ,     y(0.5) = 0.5;y(0.6), y(0.7), y(0.8), y(0.9), y(1.0)
4. y′ = xy + y²,     y(1) = 1;y(1.1), y(1.2), y(1.3), y(1.4), y(1.5)
5. Use Euler’s method to approximate y(0.2), where y(x) is the solution of the ...