Unformatted text preview: 0.8 1.6 2.4 3.2 4 4.8 5.6 6.4 7.2 8 8.8 9.6 10.415105 5 10 15 20 25 30 35 Exact Equations First Order Equations Revisited. Recall that every frst order di±erential equation is in the Form dy dx = G ( x,y ) For some Function G = G ( x,y ). Say that there are two Functions M = M ( x,y ) and N = N ( x,y ) such that G ( x,y ) = − M ( x,y ) N ( x,y ) . Then we can write the frst order di±erential equation in the Form dy dx = − M ( x,y ) N ( x,y ) = ⇒ M ( x,y ) dx + N ( x,y ) dy = 0 . Recall that a diferential equation is simply an equation involving di±erentials such as dx and dy . Since this is the Diferential Calculus we can manipulate di±erentials in this way. Such an equation will also be called a frst order di±erential equation....
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 Spring '09
 EdrayGoins
 Critical Point, Slope, lim, Monotonic function, Convex function, order differential equation

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