N- My If = R, where R is a function depending only on the quantity z = xy, then the differential equation хМ — уN M + Ny = 0 has an integrating factor of the form R(z)dz µ(z) Find an integrating factor and solve the given equation. (3x² 9y\ dy 9х + y = 0 dx + 5x2 H(xy) = ху 3xy+ + 3y3 = C 2 5x µ(xy) = xy, 3x²y + + 3y = c 2 5x µ(xy) xy' 3x y + + 3y3 = C 2 5x2 И(ху) %3D ху, Зх3 у+ + 3y = c 2 5x2 H(xy) = 3x°y + 1 3xy + ху + 3y = 2

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.