MTH422
Question: The PDE \\(x\\frac{\\partial y}{\\partial x}+y\\frac{\\partial y}{\\partial z}=0\\)\nis a linear _______ equation.
Answer: homogeneous
Question: The equation \\(x\\frac{\\partial u}{\\partial x}+y\\frac{\\partial u}{\\partial z}=sinxy\\)\nis of ______ order
Answer: is of ______ order
Question: The ______ cone at a fix point \\((x_{0},y_{0},z_{0})\\)\nin the envelope of one particular family of planes.
Answer: Monge
Question: \\(\\left ( \\frac{\\partial ^{2}u}{\\partial x^{2^{}}} \\right )^{3}+\\frac{\\partial^2 u}{\\partial y^2}+\\frac{\\partial^3 u}{\\partial x\\partial y}=0\\) is _____ order non-linear.
Answer: second
Question: \\(\\frac{\\partial^2 u}{\\partial x\\partial y}+\\left ( \\frac{\\partial u}{\\partial x} \\right )^{3}=\\frac{\\partial y}{\\partial x}+z^{3}\\) is ______ linear.
Answer: Semi
Question: A ______ relation between x and y is of the form \\(a(x,y)=0\\)\n
Answer: Single
Question: \\(u_{tt}+au_{t}+bu=c^{2}u_{xx}\\)is the ______ equation.
Answer: Telegraph
Question: The general ______ PDE of first order has the form \\(F(x,y,z,p,q)=0\\)\n
Answer: Non-linear
Question: The ______ law states that the rate of change of total substance contained ina fixed domain is equal to the flux of that substance across the boundary.
Answer: Conservation
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