1. Determine which of the following equations is linear or nonlinear. If the equation is nonlinear,...

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1. Determine which of the following equations is linear or nonlinear. If the equation is nonlinear, circle all the nonlinear terms. Also, determine the order of each equation and the independent variable used in it. Show all the work to justify your answer. (Remark: A differential equation is still called linear when it can be reduced to a linear one despite its different original form. So be extra careful!) (a) d'y dt² + e (d) (e) dy dt (b) y'+yy" = (c) etyy = 1 1 + t²y' 1+t³y" 1+x²y' 1+x³y" + t²y = Int Т = 2t = 2x + y 1. Determine which of the following equations is linear or nonlinear. If the equation is nonlinear, circle all the nonlinear terms. Also, determine the order of each equation and the independent variable used in it. Show all the work to justify your answer. (Remark: A differential equation is still called linear when it can be reduced to a linear one despite its different original form. So be extra careful!) (a) d'y dt² + e (d) (e) dy dt (b) y'+yy" = (c) etyy = 1 1 + t²y' 1+t³y" 1+x²y' 1+x³y" + t²y = Int Т = 2t = 2x + y