Question: 1. Solve the following initial value problem, y'(xy + y - 2x - 2) = In(x + 1), y(0) =0, x> -1. 2. Find a

1. Solve the following initial value problem, y'(xy + y - 2x - 2) = In(x + 1), y(0) =0, x> -1. 2. Find a special integrating factor and solve ryy' tr+ y? =0. 3. Find an integrating factor and solve (2x y + x)dy + (xy? + y)dr = 0. 4. Solve the following initial value problem, rdy + (y - y' Inx) dx = 0, y(1) = 5. Solve dx 2rdy - y = y [1 - In? (")], x>o. 6. Solve dy dx - cos? (x - y) = 0. 7. Solve (y')2 + (x + 2y) cos(x + y) = (x + 2y + cos(r + y))y'

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