Question

the differential equation having a basis for its solution as sin h6x and cos h6x is​

Answer 1

Answer:

Correct option is C)

a

2

=sin

6

x+cos

6

x

⇒a

2

=(sin

2

x+cos

2

x)(sin

4

x+cos

4

x−sin

2

xcos

2

x)

⇒a

2

=((sin

2

x+cos

2

x)

2

−3sin

2

xcos

2

x) as(sin

2

x+cos

2

x=1)

⇒a

2

=(1−3sin

2

xcos

2

x)

⇒a

2

=(1−

4

3

sin

2

2x)

sin

2

2x∈[0,1]

∴1−

4

3

sin

2

(2x)∈[

4

1

,1]

4

1

≤a

2

≤1

a∈[(−∞,

2

−1

]∪[

2

1

,∞)]∩[−1,1]

∴a∈[−1,

2

−1

]∪[

2

1

,1]