- #1
LeitHunt
Homework Statement
For an analytic function, f(x+iy)=u(x,y)+iv(x,y),u is given by u=(3x^2) -(3y^2). The expression for v, considering K to be a constant is?
Homework Equations
δu/δx=δv/δy
δu/δy=-δv/δx
[/B]
The Attempt at a Solution
My attempt :-
u=(3x^2) -(3y^2)
δu/δx=6x & δu/δy=-6y...(1)
From Relevant equations,
δu/δx=δv/δy
From (1)
6x=δv/δy
∫δv=∫6x δy
v=6xy+f(x)
From Relevant equations,
δu/δy=-δv/δx
From (1)
-6y=-δv/δx
-6y=-[δ/δx(6xy+f(x)]
6y=6y+f'(x)
f'(x)=0
Integrating,
f(x)=0+K
∴v=6xy+0+K
v=6xy+K[/B]
https://m.imgur.com/a/CDQlL
I know Partial derivative but never heard about Partial integration so first time came across this type of problem.
I checked the procedure on Internet and try to solve according to that.
In book they may have solved it wrong.
In picture on right side of red line I solved the problem according to Internet procedures and I got the same answer as book. But in book the (6x) should be partially integrate with respect to y by mistake they may have integrated with respect to x.
Which one is correct in picture solved by book or by me?
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