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

Check Equation: First, we need to check if the differential equation can be rearranged so that all terms involving y are on one side and all terms involving x are on the other side. This is the essence of separation of variables.Rewrite Equation: We start by rewriting the equation as dy = sqrt(xy) dx. Now, we need to express sqrt(xy) in a way that separates the variables.Separate Variables: We can rewrite sqrt(xy) as (x^(1/2))(y^(1/2)). This allows us to see the variables x and y multiplied under the square root, which suggests that separation of variables might be possible.Divide and Multiply: Now, we attempt to separate the variables by dividing both sides by y^(1/2) and multiplying both sides by dx/x^(1/2), which gives us (y^(-1/2)) dy = (x^(-1/2)) dx.Successful Separation: We have successfully separated the variables, with y terms on one side and x terms on the other side. This means that the differential equation can be solved using the method of separation of variables.

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Can this differential equation be solved using separation of variables?

(dy)/(dx)=sqrt(xy)
Choose 1 answer:
(A) Yes
(B) No

Can this differential equation be solved using separation of variables? $\newline$ $\frac{d y}{d x}=\sqrt{x y}$ $\newline$ 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}=\sqrt{x y}

\newline

Choose

1

answer:

\newline

(A) Yes

\newline

(B) No

Check Equation: First, we need to check if the differential equation can be rearranged so that all terms involving $y$ are on one side and all terms involving $x$ are on the other side. This is the essence of separation of variables.
Rewrite Equation: We start by rewriting the equation as $dy = \sqrt{xy} \, dx$ . Now, we need to express $\sqrt{xy}$ in a way that separates the variables.
Separate Variables: We can rewrite $\sqrt{xy}$ as $(x^{1/2})(y^{1/2})$ . This allows us to see the variables $x$ and $y$ multiplied under the square root, which suggests that separation of variables might be possible.
Divide and Multiply: Now, we attempt to separate the variables by dividing both sides by $y^{1/2}$ and multiplying both sides by $dx/x^{1/2}$ , which gives us $(y^{-1/2}) dy = (x^{-1/2}) dx$ .
Successful Separation: We have successfully separated the variables, with $y$ terms on one side and $x$ terms on the other side. This means that the differential equation can be solved using the method of separation of variables.