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The type of partial differential equation uxx+xuyy = 0, x>0 is
- a)Parabolic
- b)Hyperbolic
- c)Elliptic
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The type of partial differential equation uxx+xuyy = 0, x>0 isa)Parab...
Elliptic Partial Differential Equation
An elliptic partial differential equation is a type of PDE in which the solution is smooth and continuous. The equation involves the second-order derivatives of the dependent variable and a constant coefficient. The type of PDE is determined by the sign of the discriminant B² - 4AC of the general second-order PDE equation Ax² + Bxy + Cy² + Dx + Ey + F = 0.
The Discriminant
- If B² - 4AC > 0, then the PDE is hyperbolic
- If B² - 4AC < 0,="" then="" the="" pde="" is="" />
- If B² - 4AC = 0, then the PDE is parabolic.
Given the PDE uxx xuyy = 0, x>0, we can find A, B, and C as follows:
A = 1, B = 0, and C = -1.
Thus, B² - 4AC = 0 - 4(1)(-1) = 4 > 0.
Since B² - 4AC > 0, the PDE is not parabolic. Also, since B = 0, the PDE is not hyperbolic. Therefore, the PDE is elliptic.
Conclusion
In conclusion, the given PDE uxx xuyy = 0, x>0 is an elliptic partial differential equation.
An elliptic partial differential equation is a type of PDE in which the solution is smooth and continuous. The equation involves the second-order derivatives of the dependent variable and a constant coefficient. The type of PDE is determined by the sign of the discriminant B² - 4AC of the general second-order PDE equation Ax² + Bxy + Cy² + Dx + Ey + F = 0.
The Discriminant
- If B² - 4AC > 0, then the PDE is hyperbolic
- If B² - 4AC < 0,="" then="" the="" pde="" is="" />
- If B² - 4AC = 0, then the PDE is parabolic.
Given the PDE uxx xuyy = 0, x>0, we can find A, B, and C as follows:
A = 1, B = 0, and C = -1.
Thus, B² - 4AC = 0 - 4(1)(-1) = 4 > 0.
Since B² - 4AC > 0, the PDE is not parabolic. Also, since B = 0, the PDE is not hyperbolic. Therefore, the PDE is elliptic.
Conclusion
In conclusion, the given PDE uxx xuyy = 0, x>0 is an elliptic partial differential equation.
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Community Answer
The type of partial differential equation uxx+xuyy = 0, x>0 isa)Parab...
A second order linear partial differential equation of the form
is said to be
is said to be(i) Parabolic if B2 - 4AC = 0
(ii) Hyperbolic if B2 - 4AC > 0
(iii) Elliptic if B2 - 4AC < />
Comparing the given PDE with the above general PDE, we
get A = 1, B = 0, C = x
ஃ B2 - 4AC = (0)2 - 4(1) (x)
= - 4x < 0="" (∵="" x="" /> 0)
ஃ The type of PDE is elliptic
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The type of partial differential equation uxx+xuyy = 0, x>0 isa)Parabolicb)Hyperbolicc)Ellipticd)None of theseCorrect answer is option 'C'. Can you explain this answer?
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