1. Differential Equations Separable Examples Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

2. Use separation of variables to find the general solution to the given differential equation. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

3. Use separation of variables to find the general solution to the given differential equation. First, write the derivative in fraction form. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Next do some algebra until all the y terms are on one side and t terms are on the other:

4. Use separation of variables to find the general solution to the given differential equation. First, write the derivative in fraction form. Next do some algebra until all the y terms are on one side and t terms are on the other: typically you want to leave constants on the t side Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

5. Use separation of variables to find the general solution to the given differential equation. First, write the derivative in fraction form. Next do some algebra until all the y terms are on one side and t terms are on the other: typically you want to leave constants on the t side Now we can integrate both sides and solve for y. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

6. Use separation of variables to find the general solution to the given differential equation. First, write the derivative in fraction form. Next do some algebra until all the y terms are on one side and t terms are on the other: typically you want to leave constants on the t side Now we can integrate both sides and solve for y. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

7. Use separation of variables to find the general solution to the given differential equation. First, write the derivative in fraction form. Next do some algebra until all the y terms are on one side and t terms are on the other: typically you want to leave constants on the t side Now we can integrate both sides and solve for y. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

8. Use separation of variables to find the general solution to the given differential equation. First, write the derivative in fraction form. Next do some algebra until all the y terms are on one side and t terms are on the other: typically you want to leave constants on the t side Now we can integrate both sides and solve for y. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

9. Use separation of variables to find the general solution to the given differential equation. First, write the derivative in fraction form. Next do some algebra until all the y terms are on one side and t terms are on the other: typically you want to leave constants on the t side Now we can integrate both sides and solve for y. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB This C is really e C. Since it is still arbitrary we can still call it C.

10. Use separation of variables to find the general solution to the given differential equation. First, write the derivative in fraction form. Next do some algebra until all the y terms are on one side and t terms are on the other: typically you want to leave constants on the t side Now we can integrate both sides and solve for y. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB This C is really e C. Since it is still arbitrary we can still call it C.

11. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Use separation of variables to find the general solution to the given differential equation.

12. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Use separation of variables to find the general solution to the given differential equation.

13. We’ll need to use a substitution for the y integral: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Use separation of variables to find the general solution to the given differential equation.

14. We’ll need to use a substitution for the y integral: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Use separation of variables to find the general solution to the given differential equation.

15. We’ll need to use a substitution for the y integral: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Use separation of variables to find the general solution to the given differential equation.

16. We’ll need to use a substitution for the y integral: C is an arbitrary constant, so we can multiply by -2 and still call it C Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Use separation of variables to find the general solution to the given differential equation.

17. We’ll need to use a substitution for the y integral: C is an arbitrary constant, so we can multiply by -2 and still call it C Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Use separation of variables to find the general solution to the given differential equation.

18. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

19. Find a particular solution to the given initial value problem. First we separate and integrate Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

20. Find a particular solution to the given initial value problem. First we separate and integrate We can use a substitution for this integral Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

21. Find a particular solution to the given initial value problem. First we separate and integrate We can use a substitution for this integral Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

22. Find a particular solution to the given initial value problem. First we separate and integrate We can use a substitution for this integral Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

23. Find a particular solution to the given initial value problem. First we separate and integrate Now we can find the constant from the initial value: We can use a substitution for this integral Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

24. Find a particular solution to the given initial value problem. First we separate and integrate Now we can find the constant from the initial value: Plugging this into our general solution we get We can use a substitution for this integral Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

25. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

26. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

27. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

28. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

29. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

30. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Find C from the initial value

31. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Find C from the initial value

32. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

33. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

34. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

35. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

36. Find a particular solution to the given initial value problem. Don’t forget the +/- Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

37. Find a particular solution to the given initial value problem. Don’t forget the +/- Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

38. Find a particular solution to the given initial value problem. Don’t forget the +/- Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

39. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

40. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

41. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

42. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

43. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

44. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

45. Find a particular solution to the given initial value problem. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB