1. **Problem Statement:** Find the order and degree of the differential equation $$\frac{d^3 y}{dx^3} + \left(\frac{d^2 y}{dx^2}\right)^{10} + 3 \left(\frac{dy}{dx}\right)^7 + 8y = 0$$. 2. **Definitions:** - The **order** of a differential equation is the highest order derivative present. - The **degree** of a differential equation is the power of the highest order derivative after the equation is free from radicals and fractions with respect to derivatives. 3. **Identify the highest order derivative:** - The highest order derivative is $$\frac{d^3 y}{dx^3}$$, which is the third derivative. 4. **Determine the degree:** - The highest order derivative $$\frac{d^3 y}{dx^3}$$ appears to the first power. - There are no radicals or fractions involving derivatives. - Therefore, the degree is 1. 5. **Final answer:** - Order = 3 - Degree = 1 Thus, the differential equation is of order 3 and degree 1.