Question:
The degree of the differential equation \(y' + y = \frac{5}{y'}\) is
The degree of the differential equation \(y' + y = \frac{5}{y'}\) is
Show Hint
Don't be tempted to state the degree by just looking at the initial form of the equation. Always clear denominators and radicals involving any derivative terms before determining the degree. The order can be found from the original equation, but the degree requires this simplification step.
Updated On: Jul 1, 2026
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Question:
We need to find the degree of the given differential equation. The degree is the highest power of the highest order derivative after the equation has been made free of radicals and fractions with respect to its derivatives.
Step 2: Key Formula or Approach:
To find the degree, we must first clear any fractions or radicals involving the derivatives. The given equation has a derivative \(y'\) in the denominator.
Step 3: Detailed Explanation:
The given differential equation is:
\[ y' + y = \frac{5}{y'} \]
To eliminate the fraction, we multiply the entire equation by \(y'\):
\[ y'(y' + y) = y'\left(\frac{5}{y'}\right) \]
\[ (y')^2 + y \cdot y' = 5 \]
The equation is now a polynomial in terms of its derivatives.
First, identify the order of the equation. The highest order derivative present is \(y'\) (or \(\frac{dy}{dx}\)), so the order is 1.
Next, identify the degree. The degree is the highest power of the highest order derivative. In this equation, the highest power of \(y'\) is 2.
Therefore, the degree of the differential equation is 2.
Step 4: Final Answer:
The degree of the given differential equation is 2.
We need to find the degree of the given differential equation. The degree is the highest power of the highest order derivative after the equation has been made free of radicals and fractions with respect to its derivatives.
Step 2: Key Formula or Approach:
To find the degree, we must first clear any fractions or radicals involving the derivatives. The given equation has a derivative \(y'\) in the denominator.
Step 3: Detailed Explanation:
The given differential equation is:
\[ y' + y = \frac{5}{y'} \]
To eliminate the fraction, we multiply the entire equation by \(y'\):
\[ y'(y' + y) = y'\left(\frac{5}{y'}\right) \]
\[ (y')^2 + y \cdot y' = 5 \]
The equation is now a polynomial in terms of its derivatives.
First, identify the order of the equation. The highest order derivative present is \(y'\) (or \(\frac{dy}{dx}\)), so the order is 1.
Next, identify the degree. The degree is the highest power of the highest order derivative. In this equation, the highest power of \(y'\) is 2.
Therefore, the degree of the differential equation is 2.
Step 4: Final Answer:
The degree of the given differential equation is 2.
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