Complex Variables and Partial Differential Equations (3130005) MCQ

MCQs of Higher Order Partial Differential Equation

MCQ No - 1

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

(A)

#$$\mathrm z={\mathrm f}_1\left(\mathrm y\right)+\mathrm x\;{\mathrm f}_2\left(\mathrm y\right)$$#

(B)

#$$\mathrm z={\mathrm f}_1\left(\mathrm y\right)+\mathrm x\;{\mathrm f}_2\left(\mathrm y-\mathrm x\right)$$#

(C)

#$$\mathrm z={\mathrm f}_1\left(\mathrm y\right)+\;{\mathrm f}_2\left(\mathrm y+\mathrm x\right)$$#

(D)

none of these


C
MCQ No - 2

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

(A)

#$$-5\mathrm e^{\mathrm x+2\mathrm y}$$#

(B)

#$$5\mathrm e^{\mathrm x+2\mathrm y}$$#

(C)

#$$-3\mathrm e^{\mathrm x+2\mathrm y}$$#

(D)

#$$-\mathrm e^{\mathrm x+2\mathrm y}$$#


D
MCQ No - 3

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

(A)

#$$\left(\frac16\right)\;\cos\left(x+2y\right)$$#

(B)

#$$-\left(\frac16\right)\;\cos\left(x+2y\right)$$#

(C)

#$$\left(\frac13\right)\;\cos\left(x+2y\right)$$#

(D)

#$$-\left(\frac13\right)\;\cos\left(x+2y\right)$$#


D
MCQ No - 4

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

(A)

elliptic

(B)

parabolic

(C)

hyperbolic

(D)

none of these


C
MCQ No - 5

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

(A)

parabolic

(B)

elliptic

(C)

hyperbolic

(D)

none of these


B