Solve the given differential equation by separation of variables.

1. dy/dx = sinx

2. dy/dx = (x + 1)²

3. dx + e^2x dy = 0

4. dy – (y - 1)² dx = 0

5. x dy/dx = 4y

6. dy/dx + 2xy² = 0

7. dy/dx = e^3x+2y

8. e^x ydy/dx = e^-y + e^-2x-y

9. y ln xdy/dx = (y + 1 / x)²

10. dy/dx = (2y + 3 / 4x + 5)²

11. csc ydx + sec² x dy = 0

12. sin3x dx + 2y cos³3x dy = 0

13. (e^y + 1)² e^-y dx + (ex + 1)³ e^-x dy = 0

14. x(1 + y²)^1/2 dx = y(1 + x²)^1/2 dy

15. dS/dr = kS