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Joint Entrance Examination
Mathematics
Differential Equations
Question 331
Question 331 of 490
Medium
MCQ
The order and degree of
[
1
+
3
(
d
y
d
x
)
2
]
2
/
3
=
4
d
3
y
d
x
3
\left[1+3\left(\dfrac{dy}{dx}\right)^2\right]^{2/3}=4\dfrac{d^3y}{dx^3}
[
1
+
3
(
d
x
d
y
)
2
]
2/3
=
4
d
x
3
d
3
y
are:
A
(
1
,
2
3
)
\left(1,\dfrac23\right)
(
1
,
3
2
)
B
(
3
,
1
)
(3,1)
(
3
,
1
)
C
(
3
,
3
)
(3,3)
(
3
,
3
)
D
(
1
,
2
)
(1,2)
(
1
,
2
)
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Official solution
Cubing both sides to clear the fractional power:
[
1
+
3
(
y
′
)
2
]
2
=
[
4
y
′
′
′
]
3
\left[1+3(y')^2\right]^2=\left[4y'''\right]^3
[
1
+
3
(
y
′
)
2
]
2
=
[
4
y
′′′
]
3
; order 3, degree 3.
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