DIFFERENTIAL EQUATION: PARALLEL LINES

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Differential Equation with Coefficients Linear in Two Variables: Parallel Lines EXAMPLE OF SOLUTION (need to see in the solution) Checking if Parallel or not Use u-substitution EX. Ex. Determine if the given DEs are parallel lines or not. 1. (x+ y - 1) dy + (2x + 2y - 3) dx = 0 Check using the conditions: u = (A , x + By) OR A1 C (2) B B, Bi - 2 (1): As (3) u = (A2x + Bzy) 2 -3 2 (3) du = (A, dx + B,dy) All conditions passed. Going back to the definition, we can conclude that the DE is parallel. OR du = (Azdx + Body) #1: (x + 2y - 3)dx - (2x + 4y - 1)dy = 0 Let u = (x + 2y); du = (dx + 2dy) - dx = (du - 2dy) (u - 3)(du - 2dy) - (2u - 1) dy = 0 (u - 3) du - (2u - 6) dy - (2u - 1) dy = 0 (u - 3) du - (4u - 7) dy = 0 (u - 3) du - (4u - 7) dy = 0 4u - 7 (u - 3) 4u - 7 - du - dy = 0 (u - 3) 4u- 7 du - dy = 0 - -4u-7 du - dy = 0 1 5 4 16 In(4u - 7) -y = C - (x +2y) - In(4(x+2y) - 7) -y = C 4(x + 2y) - 5 In(4x + 8y - 7) - 16y = C 4x - By - 5 In(4x + 8y - 7) = C - Final answer\f