This question was previously asked in

BPSC Lecturer ME Held on July 2016 (Advt. 35/2014)

Option 3 : linear and homogenous

Junior Executive (ATC) Official Paper 1: Held on Nov 2018 - Shift 1

20501

120 Questions
120 Marks
120 Mins

**Explanation:**

A** partial differential equation** is that in which there are** two or more independent variables** and **partial derivatives **with respect to any of them.

- A
**partial differential equation**is said to**linear**if the**dependent variable**and its**differential coefficients**occur in**first degree only**but**not multiplied together.** - The
**general form of a linear partial differential equation**of first order is given by**Pp + Qq = R** - The equations in which the degrees of 'p' and 'q' are
**higher than one**is called**non-linear partial differential equations of the first order.** - A function is said to be
**homogeneous**if the**degree of each and every term in the function is the same.**- If
**f(kx,ky) = k**then f(x,y) is a homogeneous function with degree 'n'.^{n}f(x,y) - If
**f(x,y)**is a homogeneous function with degree 'n' then f(x,y) = \(\left\{ {\begin{array}{*{20}{c}} {{x^n}\phi \left( {\frac{y}{x}} \right)}\\ {{y^n}\varphi \left( {\frac{x}{y}} \right)} \end{array}} \right.\)

- If
- \(x\frac{{\partial z}}{{\partial x}} + y\frac{{\partial z}}{{\partial y}} = \left( {{z^2} + {x^2}} \right)\) In this equation we can observe it
**satisfies both linear and homogeneous conditions**i.e it has a**first degree**and it is**not multiplied together**and the**degree**of**each**and**every term**in the**function is the same.**