Question

The partial differential equation \(\frac{{{\partial ^2}\phi }}{{\partial {x^2}}} + \frac{{{\partial ^2}\phi }}{{\partial {y^2}}} + \left( {\frac{{\partial \phi }}{{\partial x}}} \right) + \left( {\frac{{\partial \phi }}{{\partial y}}} \right) = 0\) has
1. Degree 1 order 2
2. Degree 1 order 1
3. Degree 2 order 1
4. Degree 2 order 2

Answer 1

Correct Answer - Option 1 : Degree 1 order 2

\(\frac{{{\partial ^2}\phi }}{{\partial {x^2}}} + \frac{{{\partial ^2}\phi }}{{\partial {y^2}}} + \left( {\frac{{\partial \phi }}{{\partial x}}} \right) + \left( {\frac{{\partial \phi }}{{\partial y}}} \right) = 0\)

This is 2^nd order derivative [order = 2]

Degree = 1

\(\frac{{{\partial ^n}{\phi ^m}}}{{\partial {x^n}}} \Rightarrow\) Here maximum value of n = order,

And value of m on maximum value of n occur = degree