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Graphing and Euler's Method

Hi,

Part "a" of my problem says

"Let y = y(x) be the solution to the initial-value problem

y' = x^2 - y/3, y=y(x), y(1)=0

Use Euler's method with n = 3 steps to estimate the value of y(2) show your steps clearly..."

Anyway, I found the values and they are correct, shown below,

x_0 = 1

y_0 = 0

x_1 = 4/3

y_1 = 1/3

x_2 = 5/3

y_2 = 8/9

x_3 = 2

y_3 = 139/81

But my problem is with part b,

Attachment 27206 <- from the answer key

It' asking me to graph my values with the graph of the actual solution, which isn't given. How am I supposed to figure out what the actual solution looks like? (Sweating)

Thanks

Re: Graphing and Euler's Method

The problem does not ask you to draw the graph of the actual solution. It asks you to write the "primary relation" of the graph of the approximation to the graph of the solution. If what is below the picture is the answer, then it seems that the "primary relation" is that the first segment of the approximation is tangent to the graph of the solution.

You can see the solution in WolframAlpha.

Re: Graphing and Euler's Method

Oh wow that is easy then, thank you :)

But what does the "primary" in "primary relation" mean?