MHTCET 22 Apr 2025 Shift 1 Paper

Concept:The degree of a differential equation is defined only when it can be expressed as a polynomial in derivatives.If any derivative appears inside a transcendental function, the degree is not defined.Explanation:The given equation is:$$\frac{d^{2} y}{d x^{2}}+3\left(\frac{d y}{d x}\right)^{2}=x^{2} \log \left(\frac{d^{2} y}{d x^{2}}\right)$$Here, the highest order derivative is $\frac{d^{2} y}{d x^{2}}$.It appears both as a linear term and inside the logarithmic expression $\log \left(\frac{d^{2} y}{d x^{2}}\right)$.Since the logarithmic term cannot be removed or expressed as a polynomial in derivatives, the equation is not polynomial in the highest order derivative.Therefore, the degree of this differential equation is not defined.Answer:Option D: Not defined