Alright, so we began by streamlining and finding our streamline equation. Let's rewrite it as d lambda = DX/VX = dy/dy = DZ/DZ. Okay, let's do one example. We'll call it example and the problem is to find the streamline equation at x = y = 0. First, let's write down our VX, the X component of our velocity field which is just X in this case, and our Y component which is X times (X - 1) * y + 1. Since this is a two-dimensional flow, there is no Z component. So, we have V of X = X and V of Y = X times (X - 1) * y + 1. Now, let's plug these into our streamline equation. We get DX/DX = X = dy/dy and V of Y, which is X times (X - 1) * y + 1. The first thing I notice is that the X's cancel out, which is good. After canceling, we are left with DX = dy / (X - 1) * y + 1. Next, we can multiply both sides by X - 1 to move it to the other side. This gives us (X - 1) * DX = dy / (y + 1). Now, we have X and y on the same side with similar variables. We can integrate both sides. Integrating (X - 1) with respect to X gives us X^2/2 - X + C_0, where C_0 is our constant. On the right side, integrating dy / (y + 1) gives us Ln(y + 1) + C_1, where C_1 is another constant. To simplify the equation, let's subtract C_0 from the left side and bring it over to the right side. This gives us X^2/2 - X = Ln(y + 1) + C_1 - C_0. And there you have...

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