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JAMIA 2021 — Mathematics PYQ

JAMIA | Mathematics | 2021

The degree of the differential equation

$[1 + (\frac{d y}{d x})^{2}]^{\frac{3}{2}} = \frac{d ^{2} y}{d x ^{2}} is :$

Choose the correct answer:

Explanation

Given Equation

$\left[1 + \left(\frac{dy}{dx}\right)^2\right]^{\frac{3}{2}} = \frac{d^2y}{dx^2}$

Step 1: Rationalize the Equation

To find the degree of a differential equation, the derivatives must be free from any radicals or fractional powers.

Squaring both sides to remove the power $\frac{3}{2}$ :

$\left(\left[1 + \left(\frac{dy}{dx}\right)^2\right]^{\frac{3}{2}}\right)^2 = \left(\frac{d^2y}{dx^2}\right)^2$

$1 + \left(\frac{dy}{dx}\right)^2 = \left(\frac{d^2y}{dx^2}\right)^2$

Wait, the power $\frac{3}{2}$ becomes $3$ after squaring:

$\left[1 + \left(\frac{dy}{dx}\right)^2\right]^3 = \left(\frac{d^2y}{dx^2}\right)^2$

Step 2: Identify Order and Degree

Order: The highest derivative present is $\frac{d^2y}{dx^2}$ , so the Order = 2.

Degree: The power of the highest order derivative (after making the equation rational) is $2$ .

Final Answer:

The degree of the differential equation is 2.