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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
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B
3,1
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C
1,2
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D
3,3
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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 3
Hence order is 3 and degree is 3

Mathematics

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