Question

* Differentiate n-times the equation
(1+x²) y ₂ + (2x-1)y1 =0

using Leibnitz theorem​

Answer 1

Step-by-step explanation:

y=(sin  

−1

x)  

2

 

on differentiating wrt x we get

⇒  

dx

dy

​  

=2sin  

−1

x×  

1−x  

2

 

​  

 

1

​  

 _______ (1)

again differentiating wrt x we get

⇒  

dx  

2

 

d  

2

y

​  

=2  

(1−x  

2

)

1−x  

2

 

​  

 

1

​  

×  

1−x  

2

 

​  

 

​  

−sin  

−1

×  

2  

1−x  

2

 

​  

 

1x−2x

​  

 

(1−x  

2

)  

dx  

2

 

d  

2

y

​  

=2[1+x  

1−x  

2

 

​  

 

sin  

−1

x

​  

]

(1−x  

2

)  

dx  

2

 

d  

2

y

​  

−2x  

1−x  

2

 

​  

 

sin  

−1

x

​  

=2

From equation (1)

(1−x  

2

)  

dx  

2

 

dy  

2

 

​  

−x  

dx

dy

​  

=2