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nknikhilesh1

If y = log( X + r00t under(X²+a²), prove that

(X²+Y²)d²Y / dX²+ X.dy/dX=0

nknikhilesh1

Any one please reply me.

mukulaish

first of all buddy
at the end it is

(X2+a2)d2Y / dX2+ X.dy/dX=0

y=log{x+ root(x^2+a^2)}
differentiatin both sides wrt x...
v get

dy/dx=1/{root(x^2+a^2)}..........(1)

again differentiatin dy/dx wrt x
v get

d^2y/dx^2=-x/{x^2+a^2}^3/2...........(2)

(^ represents raised 2 the power of....)

substitutin the values from (1) and(2) in the LHS of the given question i.e.

(X2+a2)d2Y / dX2+ X.dy/dX=0

v will get LHS=0=RHS

rate if useful...
n nudge me 4 ne doubts

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