## 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

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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