The indicated function y1(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to find
a second solution y2(x) of the homogeneous equation and a particular solution yp(x) of the given nonhomogeneous equation. y'' − 7y' + 6y = x; y1 = ex
1 answer:
Answer:
y2 = (6x + 7)/36 + (Dx + E)e^x
Step-by-step explanation:
The method of reduction of order is applicable for second-order differential equations.
For a known solution y1 of a 2nd order differential equation, this method assumes a second solution in the form Uy1 which satisfies the said differential equation. It then assumes a reduced order for U'' (w' = U'').
The differential equation becomes easy to solve, and all that is left are integration and substitutions.
Check attachments for the solution to this problem.
You might be interested in
Answer:
Step-by-step explanation:
Occurrence Year seen Difference
1 1949 -
2 1956 1956 - 1949 = 7
3 1963 1963 - 1956 = 7
4 1970 1970 - 1963 = 7
Difference between each successive term of year seen = 7 years
Therefore, there is a common difference of 7 years between each successive term.
Function defining the year seen will be a linear function and will increase in the same pattern. (multiple of 7 years)
2017 - 1970 = 47 (It's not the multiple of 7)
2018 - 1970 = 48 (It's not the multiple of 7)
2019 - 1970 = 49 (multiple of 7)
2020 - 1970 = 50 (It's not the multiple of 7)
Therefore, comet will be seen next in 2019.
Option (C) will be the answer.
If a person is born in 2005
Then difference between 2005 and 1949 = 56 years
Number of times comet seen after 1949 = times
Total number of comet seen in the lifetime = 8 times