Can this differential equation be solved using separation of variables? (dy)/(dx)=sqrt(3xy+5y) Choose 1 answer: (A) Yes (B) No

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Can this differential equation be solved using separation of variables?  (dy)/(dx)=sqrt(3xy+5y) Choose 1 answer: (A) Yes (B) No

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Analyze Differential Equation: Analyze the differential equation to determine if it can be written in the form of a product of a function of x and a function of y.Separate Variables: Attempt to separate the variables by dividing both sides of the equation by sqrt(y) and moving all terms involving y to one side and all terms involving x to the other side.Check Separability: Check if the resulting expression allows for the separation of variables, meaning that each side of the equation depends on only one variable.Factor Out y: The differential equation is (dy)/(dx) = sqrt(3xy + 5y). To separate variables, we need to factor out y from the square root to see if the remaining expression inside the square root is a function of x alone. We get (dy)/(dx) = sqrt(y) * sqrt(3x + 5).Separate Variables: Now we have (dy)/(dx) = sqrt(y) * sqrt(3x + 5). We can separate the variables by dividing both sides by sqrt(y) and multiplying both sides by dx to get (1/sqrt(y)) dy = sqrt(3x + 5) dx.Conclusion: Since we have successfully expressed the differential equation in the form where one side is a function of y and the other side is a function of x, we can conclude that the differential equation can be solved using separation of variables.

Can this differential equation be solved using separation of variables? $\newline$ $\frac{d y}{d x}=\sqrt{3 x y+5 y}$ $\newline$ Choose $1$ answer: $\newline$ (A) Yes $\newline$ (B) No

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Can this differential equation be solved using separation of variables?\newlinedydx=3xy+5y \frac{d y}{d x}=\sqrt{3 x y+5 y} dxdy​=3xy+5y​\newlineChoose 111 answer:\newline(A) Yes\newline(B) No

Can this differential equation be solved using separation of variables? $\newline$ $\frac{d y}{d x}=\sqrt{3 x y+5 y}$ $\newline$ Choose $1$ answer: $\newline$ (A) Yes $\newline$ (B) No