Question

The order and degree of the differential equation \(\sqrt{\frac{\mathrm{d} y}{\mathrm{~d} x}}-4 \frac{\mathrm{~d} y}{\mathrm{~d} x}-7 x=0\) is respectively

• A. 1,2
• B. 2,1
• C. 2,2
• D. 3,1

Hint:

Remove the square root by isolating it and squaring, then read off the highest derivative and its power.

Answer 1

The Correct Option is A

Step 1: Approach
Clear the fractional power first, because degree is defined only for a polynomial in the derivatives.

Step 2: Squaring
$\sqrt{y'} = 4y' + 7x \Rightarrow y' = (4y' + 7x)^2$, which contains $(y')^2$ as its highest power.

Step 3: Conclusion
The highest derivative is of first order and appears with power 2, so order = 1 and degree = 2.

Final Answer:
Order 1 and degree 2 match option A. \[ \boxed{\text{(A) }\text{1, 2}} \]