To determine the degree of the given differential equation, let's analyze its components step by step.
The given differential equation is:
[tex]\[
\left(\frac{d^3 x}{d t^3}\right)^4 + \left(\frac{d^4 x}{d t^4}\right)^3 + y = 0
\][/tex]
1. Identify the highest order derivative:
- The derivative [tex]\(\frac{d^3 x}{d t^3}\)[/tex] is raised to the power of 4.
- The derivative [tex]\(\frac{d^4 x}{d t^4}\)[/tex] is raised to the power of 3.
- Here, [tex]\(\frac{d^4 x}{d t^4}\)[/tex] is the highest order derivative present in the equation, as it is a fourth-order derivative.
2. Determine the power of the highest order derivative:
- The highest order derivative is [tex]\(\frac{d^4 x}{d t^4}\)[/tex].
- This derivative term, [tex]\(\frac{d^4 x}{d t^4}\)[/tex], is raised to the power of 3.
3. Degree of the differential equation:
- The degree of the differential equation is defined as the highest power to which the highest order derivative is raised.
- In this case, the highest order derivative [tex]\(\frac{d^4 x}{d t^4}\)[/tex] is raised to the power of 3.
Therefore, the degree of the differential equation [tex]\(\left(\frac{d^3 x}{d t^3}\right)^4 + \left(\frac{d^4 x}{d t^4}\right)^3 + y = 0\)[/tex] is [tex]\(3\)[/tex].
