2.2 Exercises (Separable Variables) Use separation of variables to solve the differential equation. dy 1. = xy 2. Y = xe-y dx dx dy 3. 4. xyy'=x+2 dx dy 5. = y-y 6. = xy + 3x-2y-6 (Hint: try to factor the R.H.S) dt dx = 2 2y+3 (4x+5/ Find the solution of the differential equation that satisfies the given initial condition. dy 8. = x(1+y), y(1) = 3 dx 10. = x(1) = 1 dy 7. = y(0) = -4 dx 2x+1 2y y(-2) = -1 2.3 Exercises (Linear Differential Equations) Find the general solution of the given linear differential equation 12. y' = 2y + x +5 11. x+2y = 3 dx dy 13.+ 2y = 3x + 2 dx Find the solution of the differential equation that satisfies the given initial condition. 15. xy' +y = 3x, y(1) = 4 17. t=+3u, t>0 u(2)=4 dy 14.-2y=ex, y(0) = 4 dx 16. ty' + 2ty = 1, y(2) = 3