The integrating factor of the linear differential equation $\frac{d y}{d x}=\frac{1}{4 x+3 y}$ is

The integrating factor of the linear differential equation $\frac{d y}{d x}=\frac{1}{4 x+3 y}$ is
  1. $\mathrm{e}^{3 \mathrm{x}}$
  2. $\mathrm{e}^{-3 \mathrm{x}}$
  3. $\mathrm{e}^{-4 \mathrm{y}}$
  4. $\mathrm{e}^{4 \mathrm{y}}$

Solution

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 $=e^{\int-4 d y}=e^{-4 y}$

Asked in: AP EAMCET 2023 (16 May Shift 2)

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