The degree of the differential equation frac{ | vedclass

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(D) The given differential equation is $\frac{d^2y}{dx^2} + 3\left[ \frac{dy}{dx} \right]^2 = x^2 \log \left[ \frac{d^2y}{dx^2} \right]$.To define the

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None of these

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(D) The given differential equation is $\frac{d^2y}{dx^2} + 3\left[ \frac{dy}{dx} \right]^2 = x^2 \log \left[ \frac{d^2y}{dx^2} \right]$.To define the degree of a differential equation,it must be a polynomial equation in terms of its derivatives.In this equation,the term $\log \left[ \frac{d^2y}{dx^2} \right]$ involves a transcendental function of the derivative $\frac{d^2y}{dx^2}$.Because the equation cannot be expressed as a polynomial in the differential coefficients,the degree is not defined.Therefore,the correct option is $D$.

The degree of the differential equation $\frac{d^2y}{dx^2} + 3\left[ \frac{dy}{dx} \right]^2 = x^2 \log \left[ \frac{d^2y}{dx^2} \right]$ is

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