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
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Degree is the highest power of the highest order derivative after removing fractions and radicals involving derivatives.
Updated On: May 7, 2026
- \(1\)
- \(2\)
- \(3\)
- \(4\)
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The Correct Option is B
Solution and Explanation
We are given the differential equation:
\[
y'+y=\frac{5}{y'}.
\]
Here,
\[
y'=\frac{dy}{dx}.
\]
To find the degree of a differential equation, the equation must be free from fractions involving derivatives.
So multiply both sides by \(y'\):
\[
y'(y'+y)=5.
\]
Now expand:
\[
(y')^2+yy'=5.
\]
Bring all terms to one side:
\[
(y')^2+yy'-5=0.
\]
Now the equation is a polynomial in the derivative \(y'\).
The highest power of the highest order derivative is:
\[
2.
\]
Since the highest order derivative is \(y'\), and its highest power is \(2\), the degree of the differential equation is:
\[
2.
\]
Hence, the degree is
\[
2.
\]
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