Give an example for exact differential.
Answers
Answered by
1
Definition of Exact Equation
A differential equation of type
P
(
x
,
y
)
d
x
+
Q
(
x
,
y
)
d
y
=
0
is called an exact differential equation if there exists a function of two variables
u
(
x
,
y
)
with continuous partial derivatives such that
d
u
(
x
,
y
)
=
P
(
x
,
y
)
d
x
+
Q
(
x
,
y
)
d
y
.
The general solution of an exact equation is given by
u
(
x
,
y
)
=
C
,
where
C
is an arbitrary constant.
Test for Exactness
Let functions
P
(
x
,
y
)
and
Q
(
x
,
y
)
have continuous partial derivatives in a certain domain
D
.
The differential equation
P
(
x
,
y
)
d
x
+
Q
(
x
,
y
)
d
y
=
0
is an exact equation if and only if
∂
Q
∂
x
=
∂
P
∂
y
.
Answered by
1
Answer:
this is a answer of question
add me to the brainlist answer
Attachments:
Similar questions