Question

Form the differential equation from the relation

y= acos (nx +b) 
by eliminating the arbitrary

constant a, b​

Answer 1

Answer:

this is ans

Step-by-step explanation:

It contain two constant

Then, the required differential equation in second order form]

⇒

a

y

=cos(nx+b)

⇒cos

−1

(

a

y

)=(nx+b)

⇒cos

−1

(

a

y

)−na=b

differentiatew.r.tx

⇒

dx

d[cos

−1

(

a

y

)]

−

dx

d(nx)

=

dx

db

⇒

1−(

a

y

)

2

−1

×

a

1

(

dx

dy

)−n=0

⇒

1−(

a

y

)

2

−

a

1

(

dx

dy

)

=n

⇒

n

−(

dx

dy

)

=a

1−

a

2

y

2

squaringonbothsides

⇒

n

2

(

dx

dy

)

2

=a

2

−y

2

againdifferentiatew.r.ttox

⇒

n

2

1

dx

(

dx

dy

)

2

=

dx

d(a

2

)

−

dx

d(y

2

)

⇒

n

2

2

⋅(

dx

dy

)(

dx

2

d

2

y

)=0−2y

dx

dy

⇒

n

2

(

dx

2

d

2

y

)

=−y

∴⇒

n

2

(

dx

2

d

2

y

)

+y=0

Itisrequireddifferentialequation

Answer 2

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