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Question

If 2x=y15+y15and(x21)d2ydx2+λxdydx+ky=0,thenλ+K is equal to.

A
26
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B
-24
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C
-23
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D
-26
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Solution

The correct option is C -24
Given
2x=y15+y15
or
y15+y15=2x
Differentiate with respect to x on both the sides,
15.y45dydx15.y65.dydx=2

y15(y15y15)dydx=2

(y15y15)dydx=10y

(2x21)dydx=10y (1)

Again Differentiating above equation with respect to x,$
2x21d2ydx2+dydx.2.2x2x21=10dydx
(x21)d2ydx2+xdydx=5x21dydx
(x21)d2ydx2+xdydx=5.5y ( from equation (1))

On comparing with the above equation,
we get ,λ=1andk=25

So λ+k=125=24

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