Answer :

Solution :

$\overrightarrow{V}=2\left(x^2-y^2\right)\hat{i}+v\hat{j}+3\hat{k}$

u = 2(x² – y²)

v = v

w = 3

Putting the values in continuity equation

$\frac{2\partial \left({\mathrm{x}}^2-{\mathrm{y}}^2\right)}{\partial \mathrm{x}}+\frac{\partial \mathrm{v}}{\partial \mathrm{y}}+\frac{\partial \left(3\right)}{\partial \mathrm{z}}=0$

⇒ $4\mathrm{x}+\frac{\partial \mathrm{v}}{\partial \mathrm{y}}+0=0$

⇒ $\frac{\partial \mathrm{v}}{\partial \mathrm{y}}=-4\mathrm{x}$

⇒ v = -4xy + f(x,z)