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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:

Select one:
A. 3
B. 4
C. 1
D. 7


Sagot :

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].