MAT136H1 Lecture 12: 8.1 & 8.3
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Review of exponential models y(x) = ce kx ce (ce ) kx = k kx = k y. Then n(t) = n(0)e kx (from y = ce kx ) dy = k y dx dy = k y dx dn = k dt. 2 k = k = l ne l. = k ln2 k = 2 n2. A first order separable de has form: dy = g dx (y) h (x) = g + c (x)dx g (y)dy h. 1 = 2 + c i x y 3. Separating variables: o r y x y d 3 3. 1 = 6 + c x mplicit solution xplicit solution. 1 = 2 1 + c c = 2 2 = 0. = b dt dy = k y ny. = k y = elny = ekt+c = ec kt = c kt. = k + c e e t y = c kt e.
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