The general solution ofdydx=4x-3xy-3y+4 is _____

dydx=x+14-3y ⇒dy4-3y=x+1dx ⇒∫dy4-3y=∫x+1dx ⇒-13ln4-3y=x22+x+c ⇒3x22+3x+ln4-3y=c

The general solution ofdydx=4x-3xy-3y+4 is _____

dydx=x+14-3y ⇒dy4-3y=x+1dx ⇒∫dy4-3y=∫x+1dx ⇒-13ln4-3y=x22+x+c ⇒3x22+3x+ln4-3y=c

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The general solution of
$\frac{d y}{d x} = 4 x - 3 x y - 3 y + 4 i s_____$

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In $|4 - 3 y| + 3 x + {\frac{x}{2}}^{2} + c = 0$

$\ln |4 - 3 y| + 3 x + {\frac{3 x}{2}}^{2} = c$

In $|4 - 3 y| - 3 x - {\frac{3 x}{2}}^{2} + c = 0$

ln $|4 - 3 y| + x + {\frac{x}{2}}^{2} = c$

answer is B.

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Detailed Solution

$\frac{d y}{d x} = (x + 1) (4 - 3 y) \Rightarrow \frac{d y}{4 - 3 y} = (x + 1) d x \Rightarrow \int \frac{d y}{4 - 3 y} = \int (x + 1) d x \Rightarrow - \frac{1}{3} \ln (4 - 3 y) = \frac{x^{2}}{2} + x + c \Rightarrow \frac{3 x^{2}}{2} + 3 x + \ln |4 - 3 y| = c$