WBJEE · Maths · Differential Equations
The integrating factor of the first order differential equation \(x^{2}\left(x^{2}-1\right) \frac{d y}{d x}+x\left(x^{2}+1\right) y=x^{2}-1\) is
- A \(e^{x}\)
- B \(x-\frac{1}{x}\)
- C \(x+\frac{1}{x}\)
- D \(\frac{1}{x^{2}}\)
Answer & Solution
Correct Answer
(B) \(x-\frac{1}{x}\)
Step-by-step Solution
Detailed explanation
We have, \(x^{2}\left(x^{2}-1\right) \frac{d y}{d x}+x\left(x^{2}+1\right) y=x^{2}-1\) \(\Rightarrow \quad \frac{d y}{d x}+\frac{x^{2}+1}{x\left(x^{2}-1\right)} y=\frac{1}{x^{2}}\)…
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