MHTCET 18 Apr 2026 Shift 2 Paper

Concept:Order is the highest derivative present in the equation, and degree is the highest power of that derivative after removing radicals and fractional powers.Explanation:The given differential equation is $\sqrt{1+\frac{1}{(dy/dx)^2}} = \left(\frac{d^2 y}{dx^2}\right)^{3/2}$.The highest order derivative present is $\frac{d^2 y}{dx^2}$.Hence, the order of the differential equation is 2.To find the degree, radicals and fractional powers of derivatives must be removed.Squaring both sides gives $1+\frac{1}{(dy/dx)^2} = \left(\frac{d^2 y}{dx^2}\right)^3$.Multiplying both sides by $(dy/dx)^2$ gives $(dy/dx)^2 + 1 = (dy/dx)^2\left(\frac{d^2 y}{dx^2}\right)^3$.The equation is now a polynomial in derivatives.The highest order derivative $\frac{d^2 y}{dx^2}$ appears with power 3.Therefore, the degree of the differential equation is 3.Answer:Order 2, Degree 3, which matches Option A.