Q. 245.0( 2 Votes )

If x = sin, show that (1–x2)y2–xy1–a2 y = 0

Answer :

Note: y2 represents second order derivative i.e. and y1 = dy/dx


x = sin

y = ……equation 1

to prove: (1–x2)y2–xy1–a2 y = 0

We notice a second order derivative in the expression to be proved so first take the step to find the second order derivative.

Let’s find


So, lets first find dy/dx

y =

Let t = asin–1 x => []

And y = et

…….equation 2

Again differentiating with respect to x applying product rule:

Using chain rule and equation 2:

[using ]

Using equation 1 and equation 2 :

(1–x2)y2–xy1–a2y = 0……proved

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