Question

The order and degree of the differential equation \((\frac{d^3y}{dx^3})^{\frac{2}{3}}-3\frac{d^2y}{dx^2}+5\frac{dy}{dx}+4 = 0\) are respectively

• A. \(2,3\)
• B. \(3,2\)
• C. \(3\), not defined
• D. not defined, \(3\)

Hint:

Clear the fractional power first, then read off the degree.

Answer 1

The Correct Option is B

Step 1: Read the order:
The highest derivative present is the third, so order is 3.

Step 2: Rationalise:
The term $(y''')^{2/3}$ has a fractional exponent, so isolate it and cube the equation. The new equation is polynomial in derivatives.

Step 3: Degree:
On the left, $y'''$ now has exponent 2. On the right, the highest derivative is only $y''$. So the power of $y'''$ is 2 and the degree is 2.

Final Answer:
Order 3, degree 2, option (B). \[ \boxed{3,\ 2} \]