Can this differential equation be solved using separation of variables? (dy)/(dx)=(3)/(x^(2)y-8y) Choose 1 answer: (A) Yes (B) No

Check for Separation of Variables: To determine if the differential equation can be solved using separation of variables, we need to see if we can express the equation in the form of a product of a function of y and a function of x on opposite sides of the equation.Factor out y: The given differential equation is (dy)/(dx) = (3)/(x^(2)y - 8y). We want to separate the variables y and x. To do this, we need to factor out y from the denominator.Separate the Variables: Factoring y from the denominator gives us (dy)/(dx) = (3)/(y(x^(2) - 8)). Now we can separate the variables by multiplying both sides by y and dividing by (x^(2) - 8).Final Separated Equation: After separating the variables, we get y dy = (3)/(x^(2) - 8) dx. This shows that the differential equation can indeed be separated into a function of y and a function of x.Conclusion: Since we have successfully separated the variables, the answer to the question is ＂Yes＂, the differential equation can be solved using separation of variables.

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Can this differential equation be solved using separation of variables?

(dy)/(dx)=(3)/(x^(2)y-8y)
Choose 1 answer:
(A) Yes
(B) No

Can this differential equation be solved using separation of variables? $\newline$ $\frac{d y}{d x}=\frac{3}{x^{2} y-8 y}$ $\newline$ Choose $1$ answer: $\newline$ (A) Yes $\newline$ (B) No

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Q. Can this differential equation be solved using separation of variables?

\newline

\frac{d y}{d x}=\frac{3}{x^{2} y-8 y}

\newline

Choose

1

answer:

\newline

(A) Yes

\newline

(B) No

Check for Separation of Variables: To determine if the differential equation can be solved using separation of variables, we need to see if we can express the equation in the form of a product of a function of $y$ and a function of $x$ on opposite sides of the equation.
Factor out $y$ : The given differential equation is $\frac{dy}{dx} = \frac{3}{x^{2}y - 8y}$ . We want to separate the variables $y$ and $x$ . To do this, we need to factor out $y$ from the denominator.
Separate the Variables: Factoring $y$ from the denominator gives us $\frac{dy}{dx} = \frac{3}{y(x^{2} - 8)}$ . Now we can separate the variables by multiplying both sides by $y$ and dividing by $(x^{2} - 8)$ .
Final Separated Equation: After separating the variables, we get $y \, dy = \frac{3}{x^{2} - 8} \, dx$ . This shows that the differential equation can indeed be separated into a function of $y$ and a function of $x$ .
Conclusion: Since we have successfully separated the variables, the answer to the question is ＂Yes＂, the differential equation can be solved using separation of variables.