Question: Differential Equations 1. Exact and not exact. Complete solution 2. Separation of Variables. Complete solution 3. Determine the value of k. Complete solution A. Determine

Differential Equations

1. Exact and not exact. Complete solution

2. Separation of Variables. Complete solution

3. Determine the value of k. Complete solution

Differential Equations 1. Exact and not exact.

A. Determine whether the following differential equations (DE) is exact or not exact. Support your answer. (5 items x 5 points each) 1. (6x + f2) dx + f(2x - 3f)df = 0 2. (cos2f - 3x2f2) dx = (-cos2f + 2x sin2f + 2x3f)df 3. (fexf - 2f3 ) dx + (xexf - 6xf2 - 2f) df = 0 X fvx 2+ fz df = - dx Vx2 + yz 5. (2xy - tan y) dx) = (-x2 + x seczy) dy B. Find the particular solution of the following DE using separation of variables. Provide a complete solution. (3 items x 15 points each) 1. dj _ 4x+xf2 f-x2f 2. f Inx Infax + df = 0 3. x2(1 - x2) df - f dx = 0 C. Determine the value of k of the given DE below. Show your solution. (10 points) 1. (kf - 3x)dx = _*+kidf, where G = 2x and Off = 2x x ax

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