dy cos- 8. Solve the following initial value problem: V(1 ) = - (5) dx 4x -3 + 9. Solve the fooling Initial Value problem: dy 9x- - six (5) dx cosy+ 5el 10. A bacterial culture starts with 1000 bacteria and after 2 hours there are 2500 bacteria. Assuming that the culture grows at a rate proportional to its size, find the population after 6 hours. (5) dw 2t + sec t 11. Solve the following Initial value problem , W(0) =-5. (5) dt 2w 12. Determine the solution of that passes through the point (1, 2). (5) X dw 13. Solve the Initial Value Problem =tw , 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