Question: 1. Separable/exact/constant coefficient ODEs (a) Prove that every separable ODE is exact. (b) Consider the ODE ydx xdy = 0. i. Prove that this ODE

1. Separable/exact/constant coefficient ODEs (a) Prove that every separable ODE is

1. Separable/exact/constant coefficient ODEs (a) Prove that every separable ODE is exact. (b) Consider the ODE ydx xdy = 0. i. Prove that this ODE is not exact. ii. Find a suitable integrating factor to make it exact. iii. By any means possible, find the general solution. (c) By any means possible, find general solutions to the following ODEs: _ 2 I. (% k) y(x) = 0. ii. (% k)ny(x) = 0; where n 6 2+

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