Differential Equation + Taylor Polynomial + Euler's Method
Consider the differential equation for . Let be the particular solution to this differential equation with the initial condition .
a. Evaluate and at
b. Is it possible for the x-axis to be tangent to the graph of at some point? Explain why or why not.
c. Find the second-degree Taylor polynomial for about .
d. Use Euler's method, starting at with two steps of equal size, to approximate . Show the work that leads to your answer.
Thank you to anyone can help!