Can this differential equation be solved using separation of variables? (dy)/(dx)=(7-3x)e^(-y) Choose 1 answer: (A) Yes (B) No

Analyze Equation Form: Analyze the differential equation to determine if it can be written in the form of a product of a function of x and a function of y.Separate Variables: Attempt to separate the variables by moving all terms involving y to one side of the equation and all terms involving x to the other side.Rewrite Equation: Rewrite the equation as e^y dy = (7-3x) dx to separate the variables.Check Integrability: Check if both sides of the equation can be integrated independently.Apply Separation of Variables: Since we can integrate e^y dy with respect to y and (7-3x) dx with respect to x, the differential equation can be solved using separation of variables.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Can this differential equation be solved using separation of variables?

(dy)/(dx)=(7-3x)e^(-y)
Choose 1 answer:
(A) Yes
(B) No

Can this differential equation be solved using separation of variables? $\newline$ $\frac{d y}{d x}=(7-3 x) e^{-y}$ $\newline$ Choose $1$ answer: $\newline$ (A) Yes $\newline$ (B) No

View step-by-step help

Home

Math Problems

Algebra 2

Simplify expressions using trigonometric identities

Full solution

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

\newline

\frac{d y}{d x}=(7-3 x) e^{-y}

\newline

Choose

1

answer:

\newline

(A) Yes

\newline

(B) No

Analyze Equation Form: Analyze the differential equation to determine if it can be written in the form of a product of a function of $x$ and a function of $y$ .
Separate Variables: Attempt to separate the variables by moving all terms involving $y$ to one side of the equation and all terms involving $x$ to the other side.
Rewrite Equation: Rewrite the equation as $e^y \, dy = (7-3x) \, dx$ to separate the variables.
Check Integrability: Check if both sides of the equation can be integrated independently.
Apply Separation of Variables: Since we can integrate $e^y \, dy$ with respect to $y$ and $(7-3x) \, dx$ with respect to $x$ , the differential equation can be solved using separation of variables.