MHTCET 20 Apr 2026 Shift 1 Paper

Concept:The order of a differential equation is the highest derivative present; the degree is the power of that highest derivative after the equation is expressed as a polynomial in derivatives.Explanation:The given equation is$$\left(\frac{d^{3}y}{dx^{3}}\right)^{\frac{2}{3}} - 3\frac{d^{2}y}{dx^{2}} + 5\frac{dy}{dx} + 4 = 0$$The highest order derivative present is $\frac{d^{3}y}{dx^{3}}$, so the order is $3$.However, the highest derivative has a fractional power $\frac{2}{3}$, so the degree cannot be read directly.Rearrange the terms by moving everything except the fractional power term to the right side:$$\left(\frac{d^{3}y}{dx^{3}}\right)^{\frac{2}{3}} = 3\frac{d^{2}y}{dx^{2}} - 5\frac{dy}{dx} - 4$$Now cube both sides to remove the fractional power:$$\left(\frac{d^{3}y}{dx^{3}}\right)^{2} = \left(3\frac{d^{2}y}{dx^{2}} - 5\frac{dy}{dx} - 4\right)^{3}$$Now the equation is a polynomial in derivatives. The highest order derivative $\frac{d^{3}y}{dx^{3}}$ has power $2$.Hence, the degree is $2$.Answer:The order is $3$ and the degree is $2$, so the correct option is B $(3, 2)$.