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= ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

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

Open in App

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
$B^{2} - 4 A C = 0$
$B^{2} - 4 \times 3 \times 3 = 0$
$B^{2} = 36$

Suggest Corrections

Similar questions

Q. The partial differential equaiton

\frac{\partial^{2} ϕ}{\partial x^{2}} + \frac{\partial^{2} ϕ}{\partial y^{2}} + \frac{\partial ϕ}{\partial x} + \frac{\partial ϕ}{\partial y} = 0

has

Q. The number of boundary conditions required to solve the differential equation

\frac{\partial^{2} ϕ}{\partial x^{2}} + \frac{\partial^{2} ϕ}{\partial y^{2}}

Q. In a two-dimensional flow of fluid, if a velocity potential function

ϕ

exists which satisfies the relation

\frac{\partial^{2} ϕ}{\partial x^{2}} + \frac{\partial^{2} ϕ}{\partial y^{2}} = 0

, then the flow is :

Q. If

sin θ = \frac{1}{2}

and

sin ϕ = \frac{1}{3},

find the value of

sin (θ + ϕ)

and

sin (2 θ + 2 ϕ)

cos 2 θ cos 2 ϕ + {sin}^{2} (θ - ϕ) - {sin}^{2} (θ + ϕ) = cos (2 θ + 2 ϕ)

Join BYJU'S Learning Program

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