Can this differential equation be solved using separation of variables? (dy)/(dx)=2x-3y+6 Choose 1 answer: (A) Yes (B) No

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Can this differential equation be solved using separation of variables?  (dy)/(dx)=2x-3y+6 Choose 1 answer: (A) Yes (B) No

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Check Equation Form: To determine if the differential equation (dy)/(dx) = 2x - 3y + 6 can be solved using separation of variables, we need to check if it can be written in the form of (dy)/(g(y)) = f(x)(dx), where g(y) is a function of y only and f(x) is a function of x only.Attempt Variable Separation: We attempt to separate the variables by moving all terms involving y to one side and all terms involving x to the other side of the equation. (dy)/(dx) + 3y = 2x + 6 This equation does not separate into functions of y and functions of x because the term 2x + 6 cannot be isolated as a function of x only that multiplies dx, due to the presence of the term 3y on the left side.Unable to Separate Variables: Since the terms involving y cannot be completely separated from the terms involving x, the differential equation cannot be solved using the method of separation of variables.

Can this differential equation be solved using separation of variables? $\newline$ $\frac{d y}{d x}=2 x-3 y+6$ $\newline$ Choose $1$ answer: $\newline$ (A) Yes $\newline$ (B) No

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Can this differential equation be solved using separation of variables?\newlinedydx=2x−3y+6 \frac{d y}{d x}=2 x-3 y+6 dxdy​=2x−3y+6\newlineChoose 111 answer:\newline(A) Yes\newline(B) No

Can this differential equation be solved using separation of variables? $\newline$ $\frac{d y}{d x}=2 x-3 y+6$ $\newline$ Choose $1$ answer: $\newline$ (A) Yes $\newline$ (B) No