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

Check for Separation: 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 (dy)/(y) = g(x)dx, where g(x) is a function of x only.Rewrite the Equation: First, we rewrite the differential equation as dy/dx = y(2 - x).Separate Variables: Now, we attempt to separate the variables by dividing both sides of the equation by y and multiplying both sides by dx to get (1/y)dy = (2 - x)dx.Integrate Both Sides: We have successfully separated the variables, with y on one side and x on the other. This means we can integrate both sides with respect to their respective variables.Final Solution: The integral of (1/y)dy is ln|y|, and the integral of (2 - x)dx is 2x - (x^2)/2 + C, where C is the constant of integration.Thus, the solution to the differential equation after integrating both sides is ln|y| = 2x - (x^2)/2 + C.

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Can this differential equation be solved using separation of variables?

(dy)/(dx)=2y-xy
Choose 1 answer:
(A) Yes
(B) No

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

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Intermediate Value Theorem

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

\newline

\frac{d y}{d x}=2 y-x y

\newline

Choose

1

answer:

\newline

(A) Yes

\newline

(B) No

Check for Separation: 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 $(\frac{dy}{dx}) = g(x)dx$ , where $g(x)$ is a function of $x$ only.
Rewrite the Equation: First, we rewrite the differential equation as $\frac{dy}{dx} = y(2 - x)$ .
Separate Variables: Now, we attempt to separate the variables by dividing both sides of the equation by $y$ and multiplying both sides by $dx$ to get $(1/y)dy = (2 - x)dx$ .
Integrate Both Sides: We have successfully separated the variables, with $y$ on one side and $x$ on the other. This means we can integrate both sides with respect to their respective variables.
Final Solution: The integral of $(1/y)\,dy$ is $\ln|y|$ , and the integral of $(2 - x)\,dx$ is $2x - (x^2)/2 + C$ , where $C$ is the constant of integration.
Final Solution: The integral of $(1/y)\,dy$ is $\ln|y|$ , and the integral of $(2 - x)\,dx$ is $2x - (x^2)/2 + C$ , where $C$ is the constant of integration.Thus, the solution to the differential equation after integrating both sides is $\ln|y| = 2x - (x^2)/2 + C$ .

More problems from Intermediate Value Theorem

Question

Let

f

be a continuous function on the closed interval

[1,5]

, where

f(1)=1

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

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