Can this differential equation be solved using separation of variables? (dy)/(dx)=e^(x+y) 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 g(y)dy = h(x)dx, where g(y) is a function of y only and h(x) is a function of x only.Rearrange the Equation: The given differential equation is (dy)/(dx) = e^(x+y). To separate the variables, we need to move all the y terms to one side and all the x terms to the other side.Multiply by Inverses: We can rewrite the equation as e^(-y)dy = e^(-x)dx. This is done by multiplying both sides by e^(-y) and e^(-x), which are the multiplicative inverses of e^(y) and e^(x), respectively.Express in Separated Form: Now we have the equation in the form g(y)dy = h(x)dx, where g(y) = e^(-y) and h(x) = e^(-x). This means that 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)=e^(x+y)
Choose 1 answer:
(A) Yes
(B) No

Can this differential equation be solved using separation of variables? $\newline$ $\frac{d y}{d x}=e^{x+y}$ $\newline$ 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}=e^{x+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 $g(y)\,dy = h(x)\,dx$ , where $g(y)$ is a function of $y$ only and $h(x)$ is a function of $x$ only.
Rearrange the Equation: The given differential equation is $(\frac{dy}{dx} = e^{x+y})$ . To separate the variables, we need to move all the $y$ terms to one side and all the $x$ terms to the other side.
Multiply by Inverses: We can rewrite the equation as $e^{-y}\,dy = e^{-x}\,dx$ . This is done by multiplying both sides by $e^{-y}$ and $e^{-x}$ , which are the multiplicative inverses of $e^{y}$ and $e^{x}$ , respectively.
Express in Separated Form: Now we have the equation in the form $g(y)\,dy = h(x)\,dx$ , where $g(y) = e^{-y}$ and $h(x) = e^{-x}$ . This means that the differential equation can be solved using separation of variables.

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=ex+y \frac{d y}{d x}=e^{x+y} dxdy​=ex+y\newlineChoose 111 answer:\newline(A) Yes\newline(B) No

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