The general solution of the differential equation \(x\,dy = (2x^2 + 1)\,dx\), \(x \ne 0\), is (C is an arbitrary constant)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(y = x^2 + \log|x| + C\)
Dividing by x (allowed since \(x \ne 0\)) separates the variables:
\( \displaystyle dy = \frac{2x^2 + 1}{x}\,dx \)
\( \displaystyle dy = \left(2x + \frac{1}{x}\right)dx \)
Integrating both sides:
\(y = x^2 + \log|x| + C\)