Question

Degree of differential equation \(\sqrt[3]{\left(\frac{dy}{dx}\right)^{2}+5}=\frac{1+\left(\frac{dx}{dy}\right)^{3}}{\sqrt{4+\left(\frac{dy}{dx}\right)^{5}}}\) is

• A. \(37\)
• B. \(19\)
• C. \(10\)
• D. \(5\)

Hint:

Clear all radicals and fractions by writing p for dy/dx, then read the highest power of p.

Answer 1

The Correct Option is A

Step 1: Clear the denominator
Multiply by $p^{3}\sqrt{4+p^{5}}$ to get the radicals on one side of the equation.

Step 2: Find the common power
The radicals involve cube root and square root, so raising to the power $6$ removes both.

Step 3: Count the highest power
After the step the term of highest degree in $p$ is $p^{4}\cdot p^{15}\cdot p^{18}=p^{37}$, so the degree is $37$.

Final Answer:
The degree equals $37$. \[ \boxed{\text{(A) }37} \]