Analyze the solution to the initial value problem using approximation met...

Analyze the solution to the initial value problem

using approximation methods and then compare with its exact form as follows.

(a) Sketch the direction field of the differential equation and use it to guess the value of

(b) Use Euler’s method with a step size of 0.1 to find an approximation of

(c) Find a formula for on the direction field from part (a).

(d) What is the exact value of ? Compare with your approximation in part (b).

(e) Using the exact solution obtained in part (c), determine and compare with your guess in part (a).