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


Given,


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


As,


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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