The general solution of the differential equa | vedclass

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(B) Given differential equation is $2 dx + dy = (6xy + 4x - 3y) dx$. Rearranging the terms: $dy = (6xy + 4x - 3y - 2) dx$. $dy = [2x(3y + 2) - (3y + 2

Vedclass · Accepted Answer

$\log |3y + 2| = 3x^2 - 3x + c$

Vedclass · Answer

(B) Given differential equation is $2 dx + dy = (6xy + 4x - 3y) dx$. Rearranging the terms: $dy = (6xy + 4x - 3y - 2) dx$. $dy = [2x(3y + 2) - (3y + 2)] dx$. $dy = (2x - 1)(3y + 2) dx$. Separating the variables: $\frac{dy}{3y + 2} = (2x - 1) dx$. Integrating both sides: $\int \frac{1}{3y + 2} dy = \int (2x - 1) dx$. $\frac{1}{3} \log |3y + 2| = x^2 - x + C_1$. Multiplying by $3$: $\log |3y + 2| = 3x^2 - 3x + 3C_1$. Let $3C_1 = c$, then $\log |3y + 2| = 3x^2 - 3x + c$. Thus, the correct option is $B$.

The general solution of the differential equation $2 dx + dy = (6xy + 4x - 3y) dx$ is

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