Let f(x, y) = + tan(xy – x³) , find дудх x-4y5 O a. 80y4 + sec2(xy – x³)(1+ (xy – 3x³) tan(xy – x³)) (x- 4y5)3 | Ob. 80y* + sec2(xy – x³)(1+(2xy – 6x³) tan(xy – x³)) (x- 4y5)3 80y4 + sec?(xy – x)(1 + (xy – 3x³) tan(xy – x')) (x - 4y5)3 O d. 80y4 (x – 4y5)3 + sec?(xy – x³)(1 + (2xy – 6x³) tan(xy –x³))

8. Consider the function y = c₁e² cos 2x + c₂e sin 2x + c3 + C₁x + c5€¯ + c6е 2x (a) r²(r - 1)(r-2) (r + 1) (r + 2)² = 0 (b) r²(r 1)²(r - 2)(r + 1)² (r + 2)² = 0 (c) r²(r− 1)² (r² + 4)(r + 1)(r + 2)² = 0 (d) r(r² − 2r+5)(r + 1)(r + 2)² = 0 (e) r²(r² - 2r+5)(r+1)(r+ 2)² = 0 ✓ + C7xe -2x with the c, are arbitrary constants. This y is the general solution to a certain homogeneous linear first-order ODE. Which of the following is its auxiliary equation?

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If f is the function defined by f(x) = x+ cos 2x, then f(x) = %3D O -8sin 2x - sin 2x sin 2x 8cos 2x 8sin 2r