GATE Civil Engineering (CE) 2019 Shift 2 Solved Paper

Flow net for anisotropic soil.
${\mathit{k}}_{\mathit{x}}\frac{{\partial }^2\mathit{h}}{\partial {\mathit{x}}^2}+{\mathit{k}}_{\mathit{z}}\frac{{\partial }^2\mathit{h}}{\partial {\mathit{z}}^2}=0$
$\Rightarrow \frac{{\mathit{k}}_{\mathit{x}}}{{\mathit{k}}_{\mathit{z}}}\frac{{\partial }^2\mathit{h}}{\partial {\mathit{x}}^2}+\frac{{\partial }^2\mathit{h}}{\partial {\mathit{z}}^2}=0$ ....(i)
If we transformed geometry in $\mathit{x}$ direction let $\mathit{x}$ coordinate be transformed to the new coordinate ${\mathit{x}}_{\mathit{t}}$ by the transformation.
${\mathit{x}}_{\mathit{t}}=\mathit{x}\sqrt{\frac{{\mathit{k}}_{\mathit{z}}}{{\mathit{k}}_{\mathit{x}}}}$
$\Rightarrow \mathit{x}={\mathit{x}}_{\mathit{t}}\sqrt{\frac{{\mathit{k}}_{\mathit{x}}}{{\mathit{k}}_{\mathit{z}}}}$...(ii)
From eq. (i) & (ii),
$\Rightarrow \frac{{\mathit{k}}_{\mathit{x}}}{{\mathit{k}}_{\mathit{z}}}\frac{{\partial }^2\mathit{h}}{\partial {\left({\mathit{x}}_{\mathit{t}}\sqrt{\frac{{\mathit{k}}_{\mathit{x}}}{{\mathit{k}}_{\mathit{z}}}}\right)}^2}+\frac{{\partial }^2\mathit{h}}{\partial {\mathit{z}}^2}=0$
$\frac{{\partial }^2\mathit{h}}{\partial {\mathit{x}}_{\mathit{t}}^2}+\frac{{\partial }^2\mathit{h}}{\mathrm{𝜕}{\mathit{z}}^2}=0$ Hence prove
So, multiplied factor $=\sqrt{\frac{{\mathit{k}}_{\mathit{z}}}{{\mathit{k}}_{\mathit{x}}}}$