This question is about the variation of parameters we talked in class. The following parts will help you understand the nature/proof of this method and lead you to the famous so-called Green's function, from which you are just one step away. (a) First find the general solution of y" – 5y + 6y = 2e (3) by using the Undetermined Coefficient Method (namely, using the table we build in class by observing the type of the right-hand side function).
Unitary Method
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![4. This question is about the variation of parameters we talked in class. The following parts
will help you understand the nature/proof of this method and lead you to the famous
so-called Green's function, from which you are just one step away.
(a)
First find the general solution of
y" – 5y' + 6y = 2e*
by using the Undetermined Coefficient Method (namely, using the table we build
in class by observing the type of the right-hand side function).
(b)
tion of Parameter Method. Use the information you already obtained in the previous
step, solve (3) by variation of parameters.
However, do not use the formula directly. Read and mimic steps from eq. (6) to
(10) in your textbook on page 161, repeat the process by yourself. Namely, rephrase
and apply eq.(6) to (10) to your considered question.
Now we want to compare Undetermined Coefficient Method with Varia-
y" + P(x)y + Q(x)y= f(x)
(6)
Yp (x) = u1 (x)y1 (æ)+u2(x)y2(x)
(7)
=nu + y2u½] + P[y1 u{ + Y2u½] + ¥{u + ½u½ = f(x).
(8)
W1
Y2 f (x)
W2
and u,
Y1 f (æ)
W
W
W
W
Y1
W =
Y2
Y2
Y1
W1 =
(10)
W2
| y1 f(x)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc11f8c9c-cfdb-4c7d-934f-74de7874aa85%2Fa31d564c-13f7-4119-a87d-08e38685bdf4%2Fya277o_processed.png&w=3840&q=75)
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