Question

If y = Asin3x + Bcos3x then it's Differential Eq".is​

Answer 1

Explanation:

Given, y=Asin3x+Bcos3x.

Now we've,

dx

dy

=3(Acos3x−Bsin3x).....(1).

Again

dx

2

d

2

y

=−9(Asin3x+Bcosx).....(2).

Now,

dx

2

d

2

y

+4

dx

dy

+3y=10cos3x

or, −9(Asin3x+Bcos3x)+12(Acos3x−Bsin3x)+3(Asin3x+Bcos3x)=10cos3x [ Using (1) and (2)]

or, (−6A−12B)sin3x+(−6B+12A)cos3x=10cos3x.

Now comparing both sides the co-efficients of sin3x and cos3x

we get,

−6A−12B=0 or, A=−2B.....(3) and −6B+12A=10.....(4).

Then we've, from (3) and (4)

−30B=10

or, B=−

-1/3.

.

Then,

A=2/3