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Question
The degree of the differential equation \[\left( \frac{d^2 y}{d x^2} \right)^3 + \left( \frac{dy}{dx} \right)^2 + \sin\left( \frac{dy}{dx} \right) + 1 = 0\], is
Options
3
2
1
not defined
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Solution
not defined
We have,
\[\left( \frac{d^2 y}{d x^2} \right)^3 + \left( \frac{dy}{dx} \right)^2 + \sin\left( \frac{dy}{dx} \right) + 1 = 0\]
\[\text{ The highest order derivative in this equation is }\frac{d^2 y}{d^2 x}.\]
But the equation cannot be expressed as a polynomial in differential coefficient.
Hence, the degree is not defined .
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