Question

If y¹/m + y–¹/m = 2 x prove that ( x²-1) yñ+2 + ( 2n+1) xyn+1 + (n²-m²) yñ = 0

Answer 1

Answer:

We have y

1/m

+y

−1/m

=2x

⇒y

1/m

+

y

1/m

1

=2x

(y

1/m

)

2

−2xy

1/m

+1=0

Therefore, y

1/m

=x±

x

2

−1

y=[x±

x

2

−1

]

m

Thus y

1

=

x

2

−1

±m[x±

x

2

−1

]

m

=

x

2

−1

±my

⇒(x

2

−1)y

1

2

=m

2

y

2

⇒(x

2

−1)y

2

+xy

1

=m

2

y