Question4. [-/1 Points] DETAILS MY NOTES MARSVECTORCALC6 3.1.009.
Can there exist a $C^{2}$ function $f(x, y)$ with $f_{x}=2 x-3 y$ and $f_{y}=4 x+y$ ? Yes No
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5. [-/2 Points]
DETAILS MY NOTES MARSVECTORCALC6 3.1.025.
A function $u=f(x, y)$ with continuous second partial derivatives satisfying Laplace's equation $$\frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}=0$$ is called a harmonic function. Show that the function $u(x, y)=9 x^{3}-27 x y^{2}$ is harmonic. Since $\frac{\partial^{2} u}{\partial x^{2}}=$ $\square$ and $\frac{\partial^{2} u}{\partial y^{2}}=$ $\square$ ,$\frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}=0$.
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