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

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

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Concept of Separation of Variables: Understand the concept of separation of variables. Separation of variables is a method to solve differential equations, where we can separate the variables (x and y, in this case) on different sides of the equation. This is possible if we can express the equation in the form of f(y)dy = g(x)dx, where f(y) is a function of y only and g(x) is a function of x only.Attempt Variable Separation: Attempt to separate the variables in the given differential equation. We have the differential equation (dy)/(dx)=(2x+1)/(3y). To separate the variables, we need to bring all y terms to one side and all x terms to the other side. We can multiply both sides by 3y dy and dx to get 3y dy = (2x+1) dx.Check Variable Separation: Check if the variables are completely separated. After rearranging, we have 3y dy on one side and (2x+1) dx on the other side. This means that we have successfully separated the variables, with y terms on one side and x terms on the other side.Confirm Solvability: Confirm that the differential equation can be solved using separation of variables. Since we have separated the variables into the form f(y)dy = g(x)dx, where f(y) = 3y and g(x) = 2x+1, we can conclude that the differential equation can indeed be solved using the method of separation of variables.

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

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Can this differential equation be solved using separation of variables?\newlinedydx=2x+13y \frac{d y}{d x}=\frac{2 x+1}{3 y} dxdy​=3y2x+1​\newlineChoose 111 answer:\newline(A) Yes\newline(B) No

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