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)
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
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)