Consider the following partial differential equaiton 3- 2- x2-B- 2- x- y-3-2 - y2-4-0For the equation to be classified as parabolic- the value of B2 must be

3∂ ^2ϕ∂ x^2+B∂ ^2ϕ∂ x∂ y+3∂ϕ∂ y^2+4ϕ=0 Compare nbsp; nbsp; nbsp;A∂ ^2ϕ∂ x^2+B∂ ^2ϕ∂ x∂ y+C∂ϕ∂ y^2+Dϕ=0 A=3, B=?; C=3 Equation to be parabolic B^2 4AC= ...

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Byju's Answer

Standard XII

Mathematics

Normal of a Curve y = f(x)

Consider the ...

Question

Consider the following partial differential equaiton
$3 \frac{\partial^{2} ϕ}{\partial x^{2}} + B \frac{\partial^{2} ϕ}{\partial x \partial y} + 3 \frac{\partial^{2} ϕ}{\partial y^{2}} + 4 ϕ = 0$
For the equation to be classified as parabolic, the value of $B^{2}$ must be
36

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Solution

The correct option is A 36
$3 \frac{\partial^{2} ϕ}{\partial x^{2}} + B \frac{\partial^{2} ϕ}{\partial x \partial y} + 3 \frac{\partial ϕ}{\partial y^{2}} + 4 ϕ = 0$
Compare $A \frac{\partial^{2} ϕ}{\partial x^{2}} + B \frac{\partial^{2} ϕ}{\partial x \partial y} + C \frac{\partial ϕ}{\partial y^{2}} + D ϕ = 0$
$A = 3, B = ?; C = 3$
Equation to be parabolic
$B^{2} - 4 A C = 0$
$B^{2} - 4 \times 3 \times 3 = 0$
$B^{2} = 36$

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Consider the following partial differential equaiton 3∂2ϕ∂x2+B∂2ϕ∂x∂y+3∂2ϕ∂y2+4ϕ=0 For the equation to be classified as parabolic, the value of B2 must be36

The correct option is A 363∂2ϕ∂x2+B∂2ϕ∂x∂y+3∂ϕ∂y2+4ϕ=0 Compare A∂2ϕ∂x2+B∂2ϕ∂x∂y+C∂ϕ∂y2+Dϕ=0 A=3,B=?;C=3 Equation to be parabolic B2−4AC=0 B2−4×3×3=0 B2=36

Consider the following partial differential equaiton
$3 \frac{\partial^{2} ϕ}{\partial x^{2}} + B \frac{\partial^{2} ϕ}{\partial x \partial y} + 3 \frac{\partial^{2} ϕ}{\partial y^{2}} + 4 ϕ = 0$
For the equation to be classified as parabolic, the value of $B^{2}$ must be
36