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Question

The order and degree of the differential equation.
$$\left( \cfrac { { d }^{ 2 }y }{ d{ x }^{ 2 } } \right)^3 +\left( \cfrac { dy }{ dx }  \right) =\displaystyle\int  y\,  dx$$ are respectively.


A
2 and 3
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B
2 and 2
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C
3 and 1
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D
3 and 2
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Solution

The correct option is C $$3$$ and $$1$$
differentiating the given equation on both sides
we get
$$\frac { d }{ dx } (\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } )^ 3+\frac { d }{ dx } (\frac { dy }{ dx } )=\frac { d }{ dx } (\int { ydx } )$$

$$3(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } )^ 2\times \frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } +\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } =y$$
therefore the order is $$3$$ and the degree is $$1$$[since degree is the power of highest order]

Mathematics

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