Question

Q.no 18. The partial differential equation uxx + uyy = 0 is called

Answer 1

Given,

$\[{u_{xx}} + {u_{yy}} = 0\]$

Solution,

$\[\begin{array}{l}{u_{xx}} + {u_{yy}} = 0\\ \Rightarrow \frac{{{d^2}u}}{{d{x^2}}} + \frac{{{d^2}u}}{{d{y^2}}} = 0\\ \Rightarrow {\nabla ^2}u = 0\end{array}\]$

The name of this partial differential equation is Laplace equation.