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Part B (3 x 20 = 60 Marks)

6. a) Solve the system of equations: x + y + z = 6, x - y + z = 2, 2x + y - z = 1.
   b) Find the Eigen values and Eigen vectors of the matrix A = [[8, -6, 2], [-6, 7, -4], [2, -4, 3]].

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7. a) Solve (D² + 5D + 6)y = e^-2x.
   b) Solve (D² + 2D + 1)y = x sin x.
8. Solve (x²D² - xD + 4)y = x² sin(log x).
9. a) Solve (3x + 2y + 1)dx + (3x + 2y + 2)dy = 0.
   b) Find the orthogonal trajectories of the family of curves y² = cx.

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10. Trace the curve y²(a - x) = x³.
11. Find the Radius of Curvature of the curve x⁴ + y⁴ = 2 at the point (1, 1).

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