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The general solution of the differential equation $d x=(2 x+3 y-4) d y$ is
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Verified Answer
The correct answer is:
$6 y-3 \log |4 x+6 y-5|=c$
We have $\mathrm{dx}=(2 \mathrm{x}+3 \mathrm{y}-4) \mathrm{dy}$
$$
\begin{aligned}
& \Rightarrow \frac{d x}{d y}-2 x=3 y-4 \\
& \Rightarrow P=-2, Q=3 y-4 \\
& \text { now, I.F }=e--^{2 y} \\
& \Rightarrow x . I . F=\int Q d y \\
& \Rightarrow x \cdot e^{-2 y}=\frac{(3 y-4) e^{-2 y}}{-2}-\frac{3}{4} e^{-2 y}+c \\
& \Rightarrow 4 c e^{2 y}=4 x+6 y-5 \\
& \text { or C }=6 y-3 \log |4 x+6 y-5|
\end{aligned}
$$
$$
\begin{aligned}
& \Rightarrow \frac{d x}{d y}-2 x=3 y-4 \\
& \Rightarrow P=-2, Q=3 y-4 \\
& \text { now, I.F }=e--^{2 y} \\
& \Rightarrow x . I . F=\int Q d y \\
& \Rightarrow x \cdot e^{-2 y}=\frac{(3 y-4) e^{-2 y}}{-2}-\frac{3}{4} e^{-2 y}+c \\
& \Rightarrow 4 c e^{2 y}=4 x+6 y-5 \\
& \text { or C }=6 y-3 \log |4 x+6 y-5|
\end{aligned}
$$
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