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okay we are going to solve this ignition for your problem we have D by DX is equal to e to the Y times a X and then Y of zero is equal to zero so lets focus on getting the general solution first well we have dy DX like this so lets multiply 2x on both sides and thats my recommendation you should not have the differential in the denominator then when you do that they can so of course and if you look at the right hand side now we are in the X world so sex stays but e to the Y has to go away its okay I can just divide both sides by e to the Y and on the left hand side I will just put on 1 over e to the Y like that so this is pretty much how we get ready separate the variables here we have one device together and here we have the X and then DX together right so thats how you keep track of everything now we have 1 over e to the Y dy we want to integrate out and to get ready I would write this as e to the negative Y and then this is B Y and thats equal to the X part which is time x tim