Modify your program to solve some of the exercises in Section 3.2.Exercises in Section 3.2...

Modify your program to solve some of the exercises in Section 3.2.

Exercises in Section 3.2.

Exercise 1

Use Euler’s method with the prescribed Δx to approximate the solution of the initial value problem in the given interval.

when x = 0, y = 0;Δx = 0.2 and 0 ≤x ≤2.

Exercise 2

Use Euler’s method with the prescribed Δx to approximate the solution of the initial value problem in the given interval.

y′= x + y; when x = 0, y = 1; Δx = 0.1 and 0 ≤x 0 ≤1.

Exercise 3

Use Euler’s method with the prescribed Ajc to approximate the solution of the initial value problem in the given interval. Solve the problem by elementary methods and compare the approximate values of y with the correct values.

y′ = x + y; when x = 0, y = 2;Δx = 0.1 and 0≤ x ≤1.

Exercise 4

Use Euler’s method with the prescribed Ajc to approximate the solution of the initial value problem in the given interval. Solve the problem by elementary methods and compare the approximate values of y with the correct values.

y′ = x+y; when x = 1, y = 1;Δx = 0.1 and 1≤ x ≤2.

Exercise 5

Use Euler’s method with the prescribed Ajc to approximate the solution of the initial value problem in the given interval. Solve the problem by elementary methods and compare the approximate values of y with the correct values.

y′ = x + y; when x = 2, y = − 1;Δx = 0.1 and 2 ≤ x ≤3.

Exercise 6

Use Euler’s method with the prescribed Ajc to approximate the solution of the initial value problem in the given interval. Solve the problem by elementary methods and compare the approximate values of y with the correct values.

y′ = 2x − 3y; when x = 0, y = 2;Δx = 0.1 and 0 ≤x ≤1.

Exercise 7

Use Euler’s method with the prescribed Δx to approximate the solution of the initial value problem in the given interval.

y′= e−xywhen x = 0, y = 0;Δx = 0.2 and 0 ≤x ≤2.

Exercise 8

Use Euler’s method with the prescribed Δx to approximate the solution of the initial value problem in the given interval.

Use Δx = 0.1 in Exercise.

Exercise

Use Euler’s method with the prescribed Δx to approximate the solution of the initial value problem in the given interval.

y′= e−xywhen x = 0, y = 0;Δx = 0.2 and 0 ≤x ≤2.

Exercise 9

Use Euler’s method with the prescribed Δx to approximate the solution of the initial value problem in the given interval.

y′ = (1+x2 +y2)−1; when x = 0, y = 0;Δx = 0.2 and 0 ≤ x ≤2.

Exercise 10

Use Euler’s method with the prescribed Δx to approximate the solution of the initial value problem in the given interval.

UseΔx = 0.1 in Exercise.

Exercise

Use Euler’s method with the prescribed Δx to approximate the solution of the initial value problem in the given interval.

y′ = (1+x2 +y2)−1; when x = 0, y = 0;Δx = 0.2 and 0 ≤ x ≤2.

Exercise 11

Use Euler’s method with the prescribed Δx to approximate the solution of the initial value problem in the given interval.

y′ = (cosx + sin y)1/2; when x = 0, y = 1;Δx = 0.2 and 0 ≤x ≤ 2.

Exercise 12

Use Euler’s method with the prescribed Δx to approximate the solution of the initial value problem in the given interval.

Use Δx = 0.1 in Exercise

Exercise

Use Euler’s method with the prescribed Δx to approximate the solution of the initial value problem in the given interval.

y′ = (cosx + sin y)1/2; when x = 0, y = 1;Δx = 0.2 and 0 ≤x ≤ 2.