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(a) Program your computer algebra system, using Euler's method with step 0.01, to calculate $ y(2), $ where $ y $ is the solution of the initial-value problem$ y' = x^3 - y^3 y(0) = 1 $(b) Check your work by using the CAS to draw the solution curve.

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a) $f(2)=1.90195$b) The blue curve in the graph below is the solution curve for the initial condition $y(0)=1$

Calculus 2 / BC

Chapter 9

Differential Equations

Section 2

Direction Fields and Euler's Method

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A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

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(a) Program your computer …

in this problem were asked to solve a differential equation using oilers method. And that differential equation is dy dx equals X to the third minus Y to the third with Y zero equals 1. We have our step size His .01 And we're looking for Y of two. So I wrote a code in Mathematica and this is the output that I got. You can see I have the initial condition the mhm step size in the function. And when I plugged it all in I got About 1.9. So that's what I would say for the first part is that Wife too Is approximately 1.9. And then for the next part it asked to plot the solution curve. So I did that again in Mathematica. And this is the I'll put that I got so at around to get here and when I asked for the specific value, I got again 1.899 which is really close to the value, Wife two is approximately 1.9.

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