Question

The degree and order of the differential equation \[ \left( \frac{d^2 y}{dx^2} \right)^{\frac{4}{5}} = 10 \frac{dy}{dx} + 2 \] are:

• A. Degree 2, Order 5
• B. Degree 5, Order 1
• C. Degree 20, Order 2
• D. Degree 4, Order 2

Answer 1

The Correct Option is D

The order of a differential equation is determined by the highest derivative present. Here, the highest derivative is \(\frac{d^2y}{dx^2}\), so the order is 2.

The degree is defined as the power of the highest derivative when the equation is polynomial in the highest derivative. To make the equation polynomial, raise both sides to the power \(\frac{5}{4}\):

\[ \left( \frac{d^2y}{dx^2} \right)^1 = \left( 10 \frac{dy}{dx} + 2 \right)^{\frac{5}{4}}. \]

Now, the degree of the differential equation is 4.

Thus, the equation has degree = 4 and order = 2.