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Byju's Answer
Standard XII
Mathematics
Solving Homogeneous Differential Equations
The partial d...
Question
The partial differential equaiton
∂
2
ϕ
∂
x
2
+
∂
2
ϕ
∂
y
2
+
∂
ϕ
∂
x
+
∂
ϕ
∂
y
=
0
has
A
degree
1
and order
2
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B
degree
1
and order
2
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C
degree
1
and order
1
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D
degree
2
and order
2
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Solution
The correct option is
A
degree
1
and order
2
Order
=
2
(order is the highest derivative)
Degree
=
1
(exponent of highest derivative)
Suggest Corrections
0
Similar questions
Q.
Consider the following partial differential equaiton
3
∂
2
ϕ
∂
x
2
+
B
∂
2
ϕ
∂
x
∂
y
+
3
∂
2
ϕ
∂
y
2
+
4
ϕ
=
0
For the equation to be classified as parabolic, the value of
B
2
must be
Q.
In a two-dimensional flow of fluid, if a velocity potential function
ϕ
exists which satisfies the relation
∂
2
ϕ
∂
x
2
+
∂
2
ϕ
∂
y
2
=
0
, then the flow is :
Q.
cos
2
θ
cos
2
ϕ
+
sin
2
(
θ
−
ϕ
)
−
sin
2
(
θ
+
ϕ
)
=
cos
(
2
θ
+
2
ϕ
)
Q.
Show that
cos
2
θ
cos
2
ϕ
+
sin
2
(
θ
−
ϕ
)
−
sin
2
(
θ
+
ϕ
)
=
cos
(
2
θ
+
2
ϕ
)
Q.
The number of boundary conditions required to solve the differential equation
∂
2
ϕ
∂
x
2
+
∂
2
ϕ
∂
y
2
is
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