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Question
Mathematics
The differential equation of all non-horizontal lines in a plane is
Q. The differential equation of all non-horizontal lines in a plane is
4212
216
Differential Equations
Report Error
A
d
x
2
d
2
y
=
0
53%
B
d
y
2
d
2
x
=
0
7%
C
d
x
d
y
=
0
20%
D
d
y
d
x
=
0
20%
Solution:
The general equation of all non-horizontal lines in a plane is
a
x
+
b
y
=
1
, where
a
=
0
.
Now,
a
x
+
b
y
=
1
⇒
a
d
y
d
x
+
b
=
0
[Differentiating w.r.t.
y
]
⇒
a
d
y
2
d
2
x
=
0
[Differentiating w.r.t.
y
]
⇒
d
y
2
d
2
x
=
0
[
∵
a
=
0
]
Hence, the required differential equation is
d
y
2
d
2
x
=
0
.