Question

Find general solution of y''+36y=csc 3x by using variation of parameters

Answer 1

Answer:

step by step

let

y

"

+

b

(

×

)

y

,

+

c

(

×

)

y

=

0

have general solution

y

c

=

(

1

y

1

(

×

)

+

c

2

y

2

(

×

)

they a particular solution

y

"

+

b

(

×

)

y

,

t

c

(

×

)

y

=

f

(

×

)

will have the form

y

p

=

u

7y

1

+

u

2

y

2 and we find u

1and 4

2 using the following steps . recall the wronskian is

w

=

y

'

y

,

2

-

y

,

1

y

2

and v 1 = {- y2 f w d + 42= } 1 f w d t

note when using this