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Unformatted text preview: M ATH 512-M IDTERM 1 January 30, 2012, 9:30 AM - 10:18 AM No books, notes or calculators. Pages of formulas are provided. Answer all questions. Show work for all problems, simplify your answers . NAME: P ROBLEM Y OUR S CORE O UT OF 1 25 2 30 3 30 4 15 T OTAL 100 1. (25 points) For each of the following equations, answer the following ques- tions. What are the independent and dependent variables? What is the order of the equation? What is the degree of the equation? Is it linear or nonlinear? Is it homogeneous or non-homogeneous? (a) u xy = u sin x independent variables: x, y dependent variables: u order: 2 degree: 1 linear, homogeneous. (b) u xx + e y u xz sin z = u independent variables: x, y, z dependent variables: u order: 2 degree: 1 linear, homogeneous. (c) u t + uu xx + u xxt = 1 independent variables: t, x dependent variables: u order: 3 degree: 1 nonlinear, nonhomogeneous. (d) x 4 u xy + ( u y ) 4 = 0 independent variables: x, y dependent variables: u order: 2 degree: 1 nonlinear, homogeneous.nonlinear, homogeneous....
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