HOMEWORK I: SEPARABLE DIFFEQS (1) Determine whether the given differential equation is separable. Justify your an- swer. (a) = 4y² - 3y+1 (b) dy-yesty = dr 22 +2 (c) (xy²+3y²) dy- 2x dx = 0 (2) Solve the given differential equation. Express the solution implicitly if necessary. (a) dx = x(y-1) 2(x-2)(x-1) (b) (x-y) cos y dy = 2r sin y dr (c) y=ylny√√ (d) (e+4y²)=re³ (3) Solve the given initial-value problem. Express the solution implicitly if necessary. (a) zy² dr + (1-2) dy = 0, y(2) = 1 (b)+y=0, v(1) = 1. (c) dye+ dr, y(0)=0