Question

What is the order and degree of \(\frac{d^3x}{dt^3}+\left (\frac{d^2x}{dt^2} \right )^7+\left (\frac{dx}{dt} \right )^5=e^{t}\)?
1. Order = 1, Degree = 5
2. Order = 3, Degree = 1
3. Order = 2, Degree = 7
4. Order = 7, Degree = 3

Answer 1

Correct Answer - Option 2 : Order = 3, Degree = 1

Concept:

Order of a differential equation: The order of a differential equation is the order of the highest order derivative appearing in the equation.

Degree of a differential equation: The degree of a differential equation is the degree of the highest order derivative when differential coefficients are made free from radicals and fractions.

Calculation:

We have, \(\frac{d^3x}{dt^3}+\left (\frac{d^2x}{dt^2} \right )^7+\left (\frac{dx}{dt} \right )^5=e^{t}\)

Clearly, the highest order differential coefficient in this equation is \(\frac{d^3x}{dt^3}\) and its power is 1.

Therefore, the given differential equation has an order of 3 and a degree of 1.

Hence, the order is 3 and the degree is 1.