Which of the following differential equation is not of degree 1

x^{3} y_{2} + (x + x^{2}) y_{1}^{2} + e^{x} y^{3} = sin x

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y = 2 y_{1} + 3 \sqrt{1 - y_{1}^{2}}

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y_{2}^{1 / 2} + sin x y_{1} = x y = x

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\sqrt{y_{1} + y} = x + 1

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Solution

The correct option is A $y = 2 y_{1} + 3 \sqrt{1 - y_{1}^{2}}$
The degree of the equation in (A) is clearly 1.
The equation in (B) can be written as ${(y - 2 y_{1})}^{2} = 9 (1 - y_{1}^{2})$ which is of degree 2.
The equation in (C) and (D) are also of degree 1.

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