dw 13. Solve the Initial Value Problem =t'w , w(0) =a. (5) dt 14. Use the method of separation of variables to find a general solution to the differential equation ay = 2xy+3y-4x -6. (5) dx 15. Find the solution to the initial-value problem 6 =(2x+1)(y? -2y-8) with y(0)=-3 using the dx method of separation of variables. (3) 16. Solve the equation xdx + sec xsin ydy =0. (2 ) 17. A bacterial culture contains 100 cells at a certain point in time. Sixty minutes later, there are 450 cells. Assuming exponential growth, determine the number of cells present at time t. (3) 18. Solve the following Initial Value Problem xy dy = In x, y(1) =2. (2) dx