MCQs of First order partial differential equations (Complex Variables and Partial Differential Equations - 3140610)

Complex Variables and Partial Differential Equations (3140610) MCQs

MCQs of First order partial differential equations

Showing 11 to 15 out of 15 Questions

11.

The general solution of non-linear partial differential equation $p^{2} + q^{2} = 1, where p = \frac{\partial z}{\partial x} & q = \frac{\partial z}{\partial y}$ is _____ .

(a)	$z = ax \pm \sqrt{1 - a^{2}} y + b$
(b)	$z = ax \pm \sqrt{a} y + b$
(c)	$z = ax \pm ay + b$
(d)	none of these

12.

The general solution of non-linear partial differential equation $p - x = q - y, where p = \frac{\partial z}{\partial x} & q = \frac{\partial z}{\partial y}$ is _____ .

(a)	$z = {(x + a)}^{2} {(y + a)}^{2} + b$
(b)	$z = {(x + a)}^{2} + {(y + a)}^{2} + b$
(c)	$z = (x + a) + (y + a) + b$
(d)	none of these

13.

The general solution of non-linear partial differential equation $z = px + qy + pq, where p = \frac{\partial z}{\partial x} & q = \frac{\partial z}{\partial y}$ is _____ .

(a)	$z = {ax}^{2} + by + ab$
(b)	$z = ax + {by}^{2} + ab$
(c)	$z = {ax}^{2} + {by}^{2} + ab$
(d)	$z = ax + by + ab$

14.

Eliminating the arbitrary function from $z = f (\frac{y}{x})$ , then the partial differential equation formed is _____ .

(a)	$px + qy = 1$
(b)	$px + qy = 0$
(c)	$px - qy = 1$
(d)	$px - qy = 0$

15.

Eliminating arbitrary constants a, b and c from $z = ax + by + ct$ , the partial differential equation formed is _____ .

(a)	$z = x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y} + t \frac{\partial z}{\partial t}$
(b)	$z = x \frac{\partial z}{\partial x} - y \frac{\partial z}{\partial y} - t \frac{\partial z}{\partial t}$
(c)	$z = (x \frac{\partial z}{\partial x}) (y \frac{\partial z}{\partial y}) (t \frac{\partial z}{\partial t})$
(d)	none of these

Showing 11 to 15 out of 15 Questions