Question

find general solution of 2y''+18y=6 tan3t. by variation of parameter method ​

Answer 1

Answer:

Step-by-step explanation:

Let  

y

′′

+

b

(

x

)

y

′

+

c

(

x

)

y

=

0

have general solution  

y

c

=

C

1

y

1

(

x

)

+

C

2

y

2

(

x

)

.

Then a particular solution of  

y

′′

+

b

(

x

)

y

′

+

c

(

x

)

y

=

f

(

x

)

will have the form  

y p = u 1y 1 + u 2 y 2  and we find  u 1  and  u 2  using the following steps.  Recall the Wronskian is  

W = y 1 y ′ 2 − y ′ 1 y 2 , and

u 1 = ∫ − y 2 f W d t u 2 = ∫ y 1 f W d t

Note when using this