Question

The order and degree of the differential equation whose solution is \( y = cx + c^2 - 3c^3y^2 + 2 \), where \( c \) is a parameter, is:

• A. order = 4, degree = 4
• B. order = 4, degree = 1
• C. order = 1, degree = 4
• D. None of these

Hint:

To find the order and degree of a differential equation, look for the highest order derivative and ensure that the equation is linear in its derivatives for determining the degree.

Answer 1

The Correct Option is B

Step 1: The order of the differential equation is determined by the highest derivative of \( y \) that appears in the equation. Since \( y = cx + c^2 - 3c^3y^2 + 2 \), we differentiate with respect to \( x \).
Step 2: The highest derivative of \( y \) is the fourth derivative, so the order is 4. The degree is 1, as the equation is linear in the derivatives of \( y \).

Final Answer: \[ \boxed{\text{order = 4, degree = 1}} \]