Question: Solve the following separable first-order differential equations. (a) dy/dx = (x cos(3x 2 )) / 2y 2 (b) dy/dx = y 2 / (x 2

Solve the following separable first-order differential equations.

(a) dy/dx = (x cos(3x2 )) / 2y2

(b) dy/dx = y2 / (x2 + 5x 6)

Solve the following linear initial-value problem. Show all your working, and substitute back to show that your solution is correct.

(1/x) y' (x) + (1/2) y(x) = 2, y(1) = 3

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