AP EAMCET · Maths · Differential Equations
The integrating factor of the linear differential equation \(\frac{d y}{d x}=\frac{1}{4 x+3 y}\) is
- A \(\mathrm{e}^{3 \mathrm{x}}\)
- B \(\mathrm{e}^{-3 \mathrm{x}}\)
- C \(\mathrm{e}^{-4 \mathrm{y}}\)
- D \(\mathrm{e}^{4 \mathrm{y}}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{e}^{-4 \mathrm{y}}\)
Step-by-step Solution
Detailed explanation
Given \(\frac{d y}{d x}=\frac{1}{4 x+3 y}\) \(\frac{d x}{d y}=3 y+4 x \Rightarrow \frac{d x}{d y}-4 x=3 y\) Then, IF \(=e^{\int-4 d y}=e^{-4 y}\)
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