Question

# The order and degree of the differential equation $$\left ( 1\, +\, 3\, \displaystyle \frac {dy}{dx} \right )^{2/3}\, =\, 4\, \displaystyle \frac {d^3y}{dx^3}$$ are:

A
1,23
B
3,1
C
1,2
D
3,3

Solution

## The correct option is D $$3,\, 3$$$${ \left( 1+3\cfrac { dy }{ dx } \right) }^{ 2/3 }=4\cfrac { { d }^{ 3 }y }{ { dx }^{ 3 } } \\ \Rightarrow { \left( 1+3\cfrac { dy }{ dx } \right) }^{ 2 }=16{ \left( \cfrac { { d }^{ 3 }y }{ { dx }^{ 3 } } \right) }^{ 3 }$$Highest derivative is third order And power of highest order derivative is 3Hence order is 3 and degree is 3Mathematics

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