MCQs of Higher Order Partial Differential Equation (Complex Variables and Partial Differential Equations - 3130005)

Complex Variables and Partial Differential Equations (3130005) MCQs

MCQs of Higher Order Partial Differential Equation

Showing 1 to 10 out of 14 Questions

The general solution of P.D.E. $\frac{\partial^{2} z}{\partial x^{2}} - \frac{\partial^{2} z}{\partial x \partial y} = 0$ is _____.

(a)	$z = f_{1} (y) + x f_{2} (y)$
(b)	$z = f_{1} (y) + x f_{2} (y - x)$
(c)	$z = f_{1} (y) + f_{2} (y + x)$
(d)	none of these

The particular integral (P.I.) of P.D.E. $(D^{2} + DD' - 2 D'^{2}) z = 5 e^{x + 2 y}$ is _____.

(a)	$- 5 e^{x + 2 y}$
(b)	$5 e^{x + 2 y}$
(c)	$- 3 e^{x + 2 y}$
(d)	$- e^{x + 2 y}$

The particular integral (P.I.) of P.D.E. $(D^{2} - 3 DD' + 2 D'^{2}) z = \cos (x + 2 y)$ is _____.

(a)	$(\frac{1}{6}) \cos (x + 2 y)$
(b)	$- (\frac{1}{6}) \cos (x + 2 y)$
(c)	$(\frac{1}{3}) \cos (x + 2 y)$
(d)	$- (\frac{1}{3}) \cos (x + 2 y)$

The second order P.D.E. $4 \frac{\partial^{2} z}{\partial t^{2}} - 9 \frac{\partial^{2} z}{\partial t \partial x} + 5 \frac{\partial^{2} z}{\partial x^{2}} = 0$ is _____.

(a)	elliptic
(b)	parabolic
(c)	hyperbolic
(d)	none of these

The second order P.D.E. $\frac{\partial^{2} z}{\partial t^{2}} + 2 \frac{\partial^{2} z}{\partial t \partial x} + 2 \frac{\partial^{2} z}{\partial x^{2}} = 0$ is _____.

(a)	parabolic
(b)	elliptic
(c)	hyperbolic
(d)	none of these

The general solution of P.D.E. $\frac{\partial^{2} z}{\partial x^{2}} + \frac{\partial^{2} z}{\partial y^{2}} = 0$ is _____.

(a)	$z = f_{1} (y + x) + f_{2} (y - x)$
(b)	$z = f_{1} (y + i x) + f_{2} (y - i x)$
(c)	$z = f_{1} (y + i x) + x f_{2} (y - i x)$
(d)	none of these

The general solution of P.D.E. $\frac{\partial^{2} z}{\partial x^{2}} - 2 \frac{\partial^{2} z}{\partial x \partial y} + \frac{\partial^{2} z}{\partial y^{2}} = 0$ is _____ .

(a)	$z = f_{1} (y + x) + f_{2} (y + x)$
(b)	$z = f_{1} (y + x) + f_{2} (y - x)$
(c)	$z = f_{1} (y + x) + x f_{2} (y + x)$
(d)	$z = f_{1} (y + 2 x) + f_{2} (y - 2 x)$

The general solution of P.D.E. $\frac{\partial^{2} z}{\partial x^{2}} + 4 \frac{\partial^{2} z}{\partial y^{2}} = 0$ is _____.

(a)	$z = f_{1} (y + 2 ix) + f_{2} (y - 2 ix)$
(b)	$z = f_{1} (y + 2 ix) + x f_{2} (y + 2 ix)$
(c)	$z = f_{1} (y + 2 x) + f_{2} (y - 2 x)$
(d)	none of these

The particular integral (P.I) of P.D.E. $\frac{\partial^{2} z}{\partial x^{2}} + 4 \frac{\partial^{2} z}{\partial y^{2}} = \sin (x + y)$ is _____.

(a)	$- \frac{\cos (x + y)}{5}$
(b)	$\frac{\sin (x + y)}{5}$
(c)	$- \frac{\sin (x + y)}{3}$
(d)	$- \frac{\sin (x + y)}{5}$

10.

The solution of P.D.E. $\frac{\partial^{2} z}{\partial y^{2}} = 6 x^{3} y$ is _____.

(a)	$z = x^{3} y^{3} + y ϕ_{1} (x) + ϕ_{2} (x)$
(b)	$z = x^{3} y^{3} + ϕ_{1} (x) + ϕ_{2} (x)$
(c)	$z = y^{3} + y ϕ_{1} (x) + ϕ_{2} (x)$
(d)	none of these

Showing 1 to 10 out of 14 Questions