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Unformatted text preview: is an eqn. of the form M(x, y) dx + N(x, y)dy = 0 Where M and N are homogeneous functions of the same degree. Change of Variables for Homogenous Equations If M (x, y) dx + N(x, y)dy = 0 is homogeneous, then it can be changed into a separable differentia equation by the substitution y = vx where v is a differentable function of x. Orthogonal Trajectories 2 families of curves are mutually orthogonal and each curve in one of the families is called an orthogonal trajectory of the other family of curves if they intersect at right angles. Look at Figure 5.35 pg. 373. Joke Time What is Beethoven doing in his grave? Decomposing! Why does a lobster never share? Because it’s shellfish!...
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 Fall '08
 JARVIS
 Differential Equations, Calculus, Equations, Beethoven, homogeneous differential equations, Particular Solutions

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