**In Problems 3–12 use the RK4 method with to obtain a four decimal approximation of the indicated value:**

I chose to do #3: ;

When looking for our solution we are to use the most commonly used set of values for the parameters, steps to follow:

Now that we have the formula that we will be using we need to plug and play our original equations information:

Edit: for originally I came up with the solution 8 because I had placed the x and y variables in the wrong position.

**Step 1: Find **

**Step 2: Find **

Step 3: Find

Step 4: Find

Step 5: Find our

This is the Runge Kutta Method, have I mentioned that the name is fantastic? Well, it is. In our book it says, “You are advised to look carefully at the formulas in (6); note that k2 depends on

k1, k3 depends on k2, and k4 depends on k3.” I definitely recommend paying close attention to variables and where you place them. I have made multiple mistakes when placing numbers and keeping everything in line. I got it now though.