Chapter 7.2, Problem 26E

a.

To determine

To calculate: y (2) using Euler’s method with step size 0.01.

Answer to Problem 26E

  $y(2)=\mathrm{1.90195.}$

Explanation of Solution

Given information: Where y is the solution of the initial − value problem.

  $y\text{'}=x^3-y^3,y(0)=1.$

Formula used:

According to Euler’s method:

  $y(x+h)\approx y(x)+h\to 1$

Calculation:

Using the graphing utility the graph of the function $y\text{'}=x^3-y^3,y(0)=1.$ is given below.

  

From the graph

  $y(2)=\mathrm{1.90195.}$

b.

To determine

To draw: the solution curve.

Answer to Problem 26E

Explanation of Solution

Given information: Where y is the solution of the initial − value problem.

  $y\text{'}=x^3-y^3,y(0)=1.$

Calculation:

The blue curve in the graph below is the solution curve for the initial condition y (0) = 1.