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All right so we began streamlines and we found our stream line equation and just rewrite that our stream line equation was d lambda is equal to DX over VX which is also equal to dy over D Y which is equal to D Z over DZ ok so let's do one example so we'll call it example and here the problem is and they give us a velocity function or a velocity field and that velocity field is given by X I plus X times X minus 1 times y plus 1 J so kind of a big y component there but that's ok and they're asking find the streamline equation at x equals 0 y equals 0 ok so very first thing let's write down our VX our X component of our velocity field which is just X in this case and our Y component which is this big thing right here and that's equal to x times X minus 1 y plus 1 ok so that's there there's no Z component obviously this is a two dimensional flow and we have V of X is equal to X field Y is equal to X times X minus 1 times y plus 1 ok so what we do is I just plug in these into our stream line equation ok so we're going to get if we plug it in we're going to get DX over D X which is just X that's equal to dy over dy and of our V why is this thing so it's going to be x times X minus one times y plus one let's extend this line a little bit okay the very first thing I notice is that this X and this X cancel out that's good we like things cancelling out and so then we're left with DX is equal to dy over just X minus one times y plus one okay we can multiply both sides by X minus one to move this X minus one over here right so we'll get X minus 1 DX is equal to dy over y plus one all right and now we have same variables or a similar about X and X and wine why we have them on the same side we're good we can now integrate both sides okay and on this side if we integrated X minus 1 in respect to X we'll get x squared over 2 minus X plus a constant we'll call that C naught and on the right side will actually get Ln of Y plus 1 plus another another constant for this side we can call that C 1 and what I'm going to do is I'm going to subtract this constant from this side and bring it over here so we'll get x squared over 2 x squared over 2 minus X is equal to Ln of Y plus 1 plus C 1 minus C naught ok and here constant mine.