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
B
2 and 2
C
3 and 1
D
3 and 2

Solution

## The correct option is C $$3$$ and $$1$$differentiating the given equation on both sideswe 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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