Mathematics · Partial Differential Equations

Consider the following partial differential equations: (i) ∂ 2 u ∂x 2 + 2 ∂ 2 u ∂x ∂y + (1 - sgn(y)) ∂ 2 u ∂y 2 = 0 (ii) y ∂ 2 u ∂x 2 + x ∂ 2 u ∂y 2 = 0 Which of the following statements is true?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

1Equation (ii) is hyperbolic in the I and III quadrants and elliptic in the II and IV quadrants
2Equation (ii) is elliptic in the I and III quadrants and hyperbolic in the II and IV quadrants
3Equation (i) is hyperbolic for y > 0 and elliptic for y < 0✓
4Equation (i) is parabolic for y > 0 and elliptic for y < 0

Correct answer

Equation (i) is hyperbolic for y > 0 and elliptic for y < 0

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