The order and degree of the differential equation $y^{'} + (y^{''})^{2} = (x + y^{''})^{2}$ are:

2, 1

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1, 1

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2, 2

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1, 2

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Solution

The correct option is A $1, 1$
$y^{'} + {(y^{''})}^{2} = x^{2} + {(y^{''})}^{2} + 2 x y^{''}$
$\Rightarrow y^{'} - x^{2} - 2 x y^{'} = 0$
$\Rightarrow (1 - 2 x) y^{'} - x^{2} = 0$
Highest order of the derivative $= 1$
Degree $=$ Highest power of the derivative $= 1$

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