Use a technique of integration or a substitution to ­nd an explicit solution of the given differential equation or initialvalue problem.

1. dy/dx = 1 / (1 + sinx)

2. dy/dx = sin √x / √y

3. (√x + x)dy/dx = √y + y

4. dy/dx = y^2/3 –y

5. dy/dx = e^√x/y, y(1) = 4

6. dy/dx = x tan^-1 x/y, y(0) = 3