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The general solution of the equation

 is

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CSIR-UGC (NET) Mathematical Science: Held on (26 Nov 2020)
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  4. z = ϕ(|x| + |y|), ϕ ∈ C1

Answer (Detailed Solution Below)

Option 1 :
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Detailed Solution

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Explanation:

Given: i.e. xp + yq = 0

on comping with Pp + Qq = R, we have-

P = x, Q = y & R = 0

so, By Lagrange auxillary equation

 

Now dz = 0

⇒ z = c1

using first and 2nd term

 

Integrating, 

log |z| = log |y| + log c2

Hence, general sol is -

c1 ϕ(c2) or c2 = ϕ(c1) or ϕ(c1 c2) = o

⇒ z = ϕ  

⇒ option (1) correct

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