analyticity of f(x+iy)=x^3+ax^2y+bxy^2+cy^3

Question

please have a look at the question, Necessary condition for analyticity of $f(x+iy)=x^3+ax^2y+bxy^2+cy^3$ to solve the question i started from
f(x+iy)=u(x,y)+iv(x,y) since it is analytic it will hold the C-R equations.
$$ \begin{cases} u_x = 3x^2+2axy+by^2\\ u_y = ax^2+2bxy+3cy^2 \end{cases} $$
$$ \begin{cases} v_x(x,y) &= 0 \\ v_y(x,y) &= 0 \end{cases} $$
so, $$ \begin{cases} 3x^2+2axy+by^2&=0\\ ax^2+2bxy+3cy^2&=0 \end{cases} $$
ux,uy are partial derivative of u wrt x,y resp. Similarly applies for v.
After equating the equation 1 and 2, the answers comes out to be a=3,b=3,c=1
the answer seems to differ from the one that is in the given above link.

Is there some error in the answer?

Answer 1

You have to write down the real and imaginary parts of $a,b$ and $c$ and then the real and imaginary parts of $f$ to find out what $u$ and $v$ are.