2019_2 NOUN TMA3 Questions and Answers: MTH422 - Partial Differential Equation

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2019_2 NOUN TMA3 Questions and Answers: MTH422 - Partial Differential Equation

Postby Richtubor » Fri Nov 15, 2019 12:57 pm

2019_2 NOUN TMA3 Questions and Answers: MTH422 - Partial Differential Equation


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MTH422

Determine the characteristics of \

\(2u_{xx}-4u_{xy}-6u_{yy}+u_{x}=0\\)?
\\(-1\\pm 2\\)


If \\(u_{xx}+u_{yy}=0\\) in \\(x^

{2}+y^{2}<1\\), and \\(u=y^{2}x\\) on

\\(x^{2}+y^{2}=1\\), find (0, 0)?
zero



Solve the quasilinear Cauchy

problem \\(xu_{x}+yuu_{y}=-xy\\)

subject to intial condition u=5 on

xy=1?
\\(u=1+\\sqrt(28-2xy)\\)



The following is true for the

following partial different\nial

equation used in nonlinear

\nmechanics known as the

\nKorteweg-de Vries equation\\(\

\frac{\\partial w}{\\partial t}+\\frac{\

\partial^{3}w }{\\partial x^{3}}-6w\

\frac{\\partial w}{\\partial x}=0\\)?
nonlinear; third order


If \\(u_{xx}+u_{yy}=0\\) in \\(x^

{2}+y^{2}<1\\), and \\(u=3+x+y\\) on

\\(x^{2}+y^{2}=1\\), find \\(u\\left(\

\frac{1}{2}, \\frac{1}{2}\\right)\\)?
4


Transform the hyperbolic equation \

\(2u_{xx}-4u_{xy}-6u_{yy}+u_{x}\\) to a

canonical form?
\\(u_{\\xi \\eta}+\\frac{1}{16}u_{\

\eta}+\\frac{3}{16}u_{\\eta}\\)


The PDE \\(3u_{xx}+2u_{xy}+5u_

{yy}+xu_{y}=0\\) is classified as

_________?
elliptic


Which of the following satisfied the

Laplace\'s equation in the plane?
\\(x^{2}-y^{2}\\)



Determine the characteristics of \

\(4u_{xx}+12u_{xy}+9u_{yy}-2u_

{x}+u=0\\)?
\\(2y-3x\\)


Transform the parabolic equations \

\(4u_{xx}+12u_{xy}+9u_{yy}-2u_

{x}+u=0\\)?
\\(u_{\\xi\\xi}-\\frac{1}{3}u_{\\eta}+\

\frac{1}{9}u=-\\)




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