Question

Find the pde plane having equal x and y intercept

Answer 1

Answer:  

$\frac{\partial z}{\partial x}-\frac{\partial z}{\partial y}=0$

Step-by-step explanation:

We know that,

Equation of plane having intercepts a, b  and c on axes is,

$\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$

According to question, plane makes equal intercept on x and y. Therefore,

a  = b

So we have equation of plane,

$\frac{x}{a}+\frac{y}{a}+\frac{z}{c}=1\;\;\;\;\;\;\;\;...........i)$

Differentiating above equation with respect to x and y partially;

We get,

$\frac{1}{a}+\frac{1}{c}\frac{\partial z}{\partial x}=0\\\;\\\text{and}\\\;\\\frac{1}{a}+\frac{1}{c}\frac{\partial z}{\partial y}=0$

On subtracting above equations,

We get,

$\frac{1}{c}\frac{\partial z}{\partial x}-\frac{1}{c}\frac{\partial z}{\partial y}=0\\\;\\\frac{\partial z}{\partial x}-\frac{\partial z}{\partial y}=0$

This is the required partial differential equation.