Match each differential equation problem in Column I with its result in Column II. Column I (A) x dy = y(dx + y dy), y(1) = 1 and y(x0) = -3; find x0. (B) y(t) solves (t + 1) dy/dt - t*y = 1, y(0) = -1; find y(1). (C) (x² + y²) dy = x*y dx, y(1) = 1 and y(x0) = e; find x0 (x0 0). (D) dy/

Question

Match each differential equation problem in Column I with its result in Column II. Column I (A) x dy = y(dx + y dy), y(1) = 1 and y(x0) = -3; find x0. (B) y(t) solves (t + 1) dy/dt - t*y = 1, y(0) = -1; find y(1). (C) (x² + y²) dy = x*y dx, y(1) = 1 and y(x0) = e; find x0 (x0 > 0). (D) dy/dx + 2y/x = 0, y(1) = 1; find y(2). Column II (p) 1/4 (q) -15 (r) -1/2 (s) sqrt(3)*e

Accepted Answer

A-q, B-r, C-s, D-p. Each ODE is solved with the standard method (exact/grouping, integrating factor, homogeneous substitution, separation) and the given initial condition fixes the constant; then evaluate at the requested point.

Solution

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