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

Identify Differential Equation: Identify the differential equation. The given differential equation is (dy)/(dx) = xy + 5x.Check Equation Form: Check if the equation can be written in the form of a product of a function of x and a function of y. The right-hand side of the equation, xy + 5x, cannot be expressed as a product of a function of x and a function of y because the term 5x does not contain y.Determine Separation Feasibility: Determine if separation of variables is possible. Separation of variables requires that the equation can be written in the form (dy)/(dx) = g(y) * h(x), where g(y) is a function of y only and h(x) is a function of x only. Since the term 5x cannot be separated into a function of y, separation of variables is not possible for this differential equation.

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Can this differential equation be solved using separation of variables?

(dy)/(dx)=xy+5x
Choose 1 answer:
(A) Yes
(B) No

Can this differential equation be solved using separation of variables? $\newline$ $\frac{d y}{d x}=x y+5 x$ $\newline$ 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}=x y+5 x

\newline

Choose

1

answer:

\newline

(A) Yes

\newline

(B) No

Identify Differential Equation: Identify the differential equation. $\newline$ The given differential equation is $\frac{dy}{dx} = xy + 5x$ .
Check Equation Form: Check if the equation can be written in the form of a product of a function of $x$ and a function of $y$ . The right-hand side of the equation, $xy + 5x$ , cannot be expressed as a product of a function of $x$ and a function of $y$ because the term $5x$ does not contain $y$ .
Determine Separation Feasibility: Determine if separation of variables is possible. Separation of variables requires that the equation can be written in the form $\frac{dy}{dx} = g(y) \cdot h(x)$ , where $g(y)$ is a function of $y$ only and $h(x)$ is a function of $x$ only. Since the term $5x$ cannot be separated into a function of $y$ , separation of variables is not possible for this differential equation.