Discussion
For the linear equation \( \dfrac{dy}{dx} + Py = Q \) with \( P \) a function of \( x \), the integrating factor is
Answer: D
Multiplying by \( \mu = e^{\int P dx} \) makes the left side an exact derivative:
\[ \frac{d}{dx}\left(\mu y\right) \;=\; \mu\left(y' + Py\right) \;=\; \mu Q, \]
so \( \mu y = \int \mu Q\,dx \). The negative exponent would undo the grouping rather than create it, and the factor must be built from \( P \), the coefficient of \( y \), not from the right-hand side
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development