Problems Collection of Differential Equation II

1. 0
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Problems Collection
Differential Equation II
Meiva Marthaulina
4103312019

2. 1
Determine the solution of :
1.
With y(0) = 0 and y’(0) = 1
Solution :
Eq :
To find the root
To determine the case
Since so we take case 1 that
To determine y(0) = 0
... (1)
To determine y’(0)=1
y’(t)=
y’(0)=1
... (2)
To subsitute (1) to (2)

3. 2
Conclusion
So, we get :
2.
With y(0) = 0 and y’(0) = 1
Solution :
Eq :
To find the root
To determine the case
Since so we take case 1 that
To determine y(0) = 0
... (1)
To determine y’(0)=1
y’(t)=
y’(0)=1

4. 3
... (2)
To subsitute (2) to (1)
Conclusion
So, we get :
3.
With y(0) = 0 and y’(0) = 1
Solution :
Eq :
To find the root
To determine the case
Since so we take case 1 that
To determine y(0) = 0
... (1)

5. 4
To determine y’(0)=1
y’(t)=
y’(0)=1
... (2)
To subsitute (1) to (2)
Conclusion
So, we get :
4.
Solution :
Eq :
To find the root

6. 5
To determine the case
Since the root is imaginer so we take case 3 that
Conclusion
So, we get :
5.
Solution :
Eq :
To find the root
To determine the case
Since the imaginer root so we take case 3 that

7. 6
Conclusion
So, we get :
) +
6.
Solution :
Eq :
To find the root
To determine the case
Since is real number so we take case 1 that and is imaginer and
take case 3
Conclusion
So, we get :
7.
Solution :
Eq :

8. 7
To find the root
To determine the case
Since the imaginer root so we take case 3
Conclusion
So, we get :
8.
Solution :
Eq :
To find the root

9. 8
To determine the case
Since the imaginer root so we take case 3
Conclusion
So, we get :
9.
y(0) = 0 , y’(0) = 1 , y’’(0) = 2
solution :
Eq :
To find the root
To determine the case
To find the value of

10. 9
To find constanta
y(0) = 0
0 =
... (1)
y’(0) = 1
... (2)
y’’(0) = 2
... (3)
Doing elimination
(1) and (3)
-

11. 10
Equation 1
Equation 2
Conclusion
So, we get :
10.
y(0) = y’(0) = y’’(0) = y’’’(0) = 1
solution :
eq :
To find the root
By horner method, we get the roots are 3 and -3, so we have :

12. 11
To determine the case
To find the value of
To find constanta
y(0) = 0
0 =
... (1)
y’(0) = 1
... (2)
y’’(0) = 1

13. 12
... (3)
y’’’(0) = 1
... (4)
Doing elimination
(1) and (2)
-
... (5)
(5) and (3)
-
... (6)
(2) and (3)

14. 13
-
... (7)
(1) and (7)
-
... (8)
(8) and (6)
-
Subtitute to equation (6)
Subtitute to equation (1)

15. 14
Subtitute to equation (3)
Conclusion
So, we get :
11.
q(0) = q’(0) = 0
solution :
Eq :
To find the root

16. 15
To determine the case
To find the value of
To find constanta
y(0) = 0
0 =
... (1)
y’(0) = 0
... (2)

17. 16
Equation (1)
Conclusion
So, we get :
12.
y(0) = y’(0) = 0
solution :
Eq :
To find the root

18. 17
To determine the case
To find the value of
(1)
(2)
(3)
(4)

19. 18
To find constanta
y(0) = 1
1 =
... (1)
y’(0) = 1
... (2)
Equation (1)
Conclusion
So, we get :

20. 19
13.
solution :
Eq :
To find the root
To determine the case
To find the value of
(1)

21. 20
(2)
(3)
To find constanta
y(0) = 0
0 =
Conclusion
So, we get :

22. 21
14.
solution :
Eq :
To find the root
By horner method is gotten
, and
To determine the case
To find the value of
(1)

23. 22
(2)
(3)
To find constanta
y(0) = 0
0 =
... (1)
y’(0) = 0

24. 23
Equation (1) and (3)
__
Equation (1)
Equation (2)

25. 24
Conclusion
So, we get :