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Question: Answered & Verified by Expert
The integrating factor of the linear differential equation $\frac{d y}{d x}=\frac{1}{4 x+3 y}$ is
MathematicsDifferential EquationsAP EAMCETAP EAMCET 2023 (16 May Shift 2)
Options:
  • A $\mathrm{e}^{3 \mathrm{x}}$
  • B $\mathrm{e}^{-3 \mathrm{x}}$
  • C $\mathrm{e}^{-4 \mathrm{y}}$
  • D $\mathrm{e}^{4 \mathrm{y}}$
Solution:
2208 Upvotes Verified Answer
The correct answer is: $\mathrm{e}^{-4 \mathrm{y}}$
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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