Q. 255.0( 1 Vote )

# If log y = tan–1 X, show that : (1+x2)y2+(2x–1) y1=0.

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

Given,

log y = tan–1 X

y = ……equation 1

to prove : (1+x2)y2+(2x–1)y1=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

Using chain rule, we will differentiate the above expression

Let t = tan–1 x => []

And y = et

…….equation 2

Again differentiating with respect to x applying product rule:

Using chain rule we will differentiate the above expression-

[using & ]

Using equation 2 :

(1+x2)y2+(2x–1)y1=0 ……proved

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