Question: Topic: Linear Systems - Geometry and Algebraic Techniques; Matrix Algebra and Determinants (2) The definition of an integrating factor for the differential equation P +

Topic: Linear Systems - Geometry and Algebraic Techniques; Matrix Algebra and Determinants

(2) The definition of an integrating factor for the differential equation P + Qy' = 0 is a function u(x, y) for which u(x, y) P + u(x, y) Qy' = 0 is exact. The DE (3x2 + 5xy?) dy + 3xy + 2y3 = 0 dx is NOT exact. Find numbers p, q for which u(x, y) = xPy is an integrating factor for the DE above. Then solve the equation. (3) Find all functions f(x) such that the differential equation y sin x + yf (x) dy = 0 dx is exact. Plug in an arbitrary such function and find the solution of the equation. (You are solving the DE for all of the functions f(x) all at once.) (4) Solve et/y (y - t)y' ty(1 + et/y) = 0

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