Classify the following partial differential equations:(i) ๐2๐ข๐๐ฅ2 + 3 ๐2๐ข๐๐ฆ2 = ๐๐ข
Question
Solution 1
The given partial differential equation is:
๐ยฒ๐ข/๐๐ฅยฒ + 3 ๐ยฒ๐ข/๐๐ฆยฒ = ๐๐ข
To classify this PDE, we need to look at the highest order derivatives. In this case, we have second order derivatives with respect to x and y.
The general form of a second order PDE is:
A(๐ยฒ๐ข/๐๐ฅยฒ) + B(๐ยฒ๐ข/๐๐ฆยฒ) + C(๐๐ข/๐๐ฅ) + D(๐ Knowee AI is a powerful AI-powered study tool designed to help you to s
) + C(๐๐ข/๐๐ฅ) + D(๐ Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem. Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem. Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem. Knowee AI is a powerful AI-powered study tool designed to help you to solve study p
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Classify the following partial differential equations:(i) ๐2๐ข๐๐ฅ2 + 3 ๐2๐ข๐๐ฆ2 = ๐๐ข
If ๐ข = ๐ฅ2 tanโ1 ๐ฆ๐ฅ โ ๐ฆ2 tanโ1 ๐ฅ๐ฆ show that ๐2๐ข๐๐ฅ๐๐ฆ = ๐ฅ2โ๐ฆ2๐ฅ2+๐ฆ2 and ๐2๐ข๐๐ฅ๐๐ฆ = ๐2๐ข๐๐ฆ๐๐ฅ.
7. Find the gradient for the function ๐ข = ๐(๐), ๐ = โ๐ฅ2 + ๐ฆ2 + ๐ง2.Answer: ๐๐ข = ๐โฒ(๐) ๐๐ .
Numerical Solution of Partial Differential equations: Parabolic, Hyperbolic, and elliptic equations
Use implicit differentiation to find the equation of the tangent line to the curve ๐ฅ2 + ๐ฅ๐ฆ + ๐ฆ2 = 3 at the point (1,1).
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