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in this video well be solving this differential equation given the initial condition that p of 0 is equal to 3.9 so first i dont like these decimals so im going to convert them into simplified fractions and so this is looking much better for me to work with and notice that this is a separable differential equation so i can divide this entire right side to both sides and then multiply both sides by dt now this is looking pretty messy here so im going to factor out by the largest denominator of the two so in this case its a hundred thousand and im also going to factor out the negative because i want this p squared to be positive so factor out a negative one over a hundred thousand and notice that its 17 p squared minus 3 180 p inside and so 1 over negative 1 over 100 000 is just negative 100 000 and yeah i this looks a lot better so its more manageable now at this point we can do a couple things we can either complete the square by factor on a 17 but truthfully thats going to b