Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

Can this differential equation be solved using separation of variables?\newlinedydx=3exy \frac{d y}{d x}=3 e^{x y} \newlineChoose 11 answer:\newline(A) Yes\newline(B) No

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Calculusright chevron icon
Intermediate Value Theoremright chevron icon

Full solution

Q. Can this differential equation be solved using separation of variables?\newlinedydx=3exy \frac{d y}{d x}=3 e^{x y} \newlineChoose 11 answer:\newline(A) Yes\newline(B) No
  1. 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 a function of yy times dydy equals a function of xx times dxdx.
  2. Rewrite the Differential Equation: We start by rewriting the given differential equation as dy=3exydxdy = 3e^{xy} dx.
  3. Attempt to Separate Variables: Next, we attempt to separate the variables by dividing both sides of the equation by exye^{xy}, which would give us (1/exy)dy=3dx(1/e^{xy}) dy = 3 dx. However, this is not a separation of variables because the term exye^{xy} contains both xx and yy, and we cannot isolate yy terms on one side and xx terms on the other side.
  4. Conclusion: Unable to Separate Variables: Since we cannot separate the variables into a product of a function of yy and dydy equal to a function of xx and dxdx, the differential equation cannot be solved using the method of separation of variables.

More problems from Intermediate Value Theorem

Question
Let f f be a continuous function on the closed interval [1,5] [1,5] , where f(1)=1 f(1)=1 and f(5)=−3 f(5)=-3 .\newlineWhich of the following is guaranteed by the Intermediate Value Theorem?\newlineChoose 11 answer:\newline(A) f(c)=2 f(c)=2 for at least one c c between −3-3 and 11\newline(B) f(c)=−2 f(c)=-2 for at least one c c between −3-3 and 11\newline(C) f(c)=2 f(c)=2 for at least one c c between 11 and 55\newline(D) f(c)=−2 f(c)=-2 for at least one c c between 11 and 55
Get tutor helpright-arrow

Posted 9 months ago

Question
Let h h be a continuous function on the closed interval [−3,4] [-3,4] , where h(−3)=−1 h(-3)=-1 and h(4)=2 h(4)=2 .\newlineWhich of the following is guaranteed by the Intermediate Value Theorem?\newlineChoose 11 answer:\newline(A) h(c)=1 h(c)=1 for at least one c c between −3-3 and 44\newline(B) h(c)=−2 h(c)=-2 for at least one c c between −3-3 and 44\newline(C) h(c)=−2 h(c)=-2 for at least one c c between −1-1 and 22\newline(D) h(c)=1 h(c)=1 for at least one c c between −1-1 and 22
Get tutor helpright-arrow

Posted 9 months ago

Question
Let g g be a continuous function on the closed interval [−3,3] [-3,3] , where g(−3)=0 g(-3)=0 and g(3)=6 g(3)=6 .\newlineWhich of the following is guaranteed by the Intermediate Value Theorem?\newlineChoose 11 answer:\newline(A) g(c)=−2 g(c)=-2 for at least one c c between −3-3 and 33\newline(B) g(c)=−2 g(c)=-2 for at least one c c between 00 and 66\newline(C) g(c)=5 g(c)=5 for at least one c c between −3-3 and 33\newline(D) g(c)=5 g(c)=5 for at least one c c between 00 and 66
Get tutor helpright-arrow

Posted 9 months ago

Question
Let g g be a continuous function on the closed interval [−1,4] [-1,4] , where g(−1)=−4 g(-1)=-4 and g(4)=1 g(4)=1 .\newlineWhich of the following is guaranteed by the Intermediate Value Theorem?\newlineChoose 11 answer:\newline(A) g(c)=3 g(c)=3 for at least one c c between −1-1 and 44\newline(B) g(c)=−3 g(c)=-3 for at least one c c between −4-4 and 11\newline(C) g(c)=3 g(c)=3 for at least one c c between −4-4 and 11\newline(D) g(c)=−3 g(c)=-3 for at least one c c between −1-1 and 44
Get tutor helpright-arrow

Posted 9 months ago

Question
Let g g be a continuous function on the closed interval [−1,3] [-1,3] , where g(−1)=−2 g(-1)=-2 and g(3)=−5 g(3)=-5 .\newlineWhich of the following is guaranteed by the Intermediate Value Theorem?\newlineChoose 11 answer:\newline(A) g(c)=−3 g(c)=-3 for at least one c c between −5-5 and −2-2\newline(B) g(c)=0 g(c)=0 for at least one c c between −5-5 and −2-2\newline(C) g(c)=0 g(c)=0 for at least one c c between −1-1 and 33\newline(D) g(c)=−3 g(c)=-3 for at least one c c between −1-1 and 33
Get tutor helpright-arrow

Posted 9 months ago

Question
Let f f be a continuous function on the closed interval [−2,1] [-2,1] , where f(−2)=3 f(-2)=3 and f(1)=6 f(1)=6 .\newlineWhich of the following is guaranteed by the Intermediate Value Theorem?\newlineChoose 11 answer:\newline(A) f(c)=0 f(c)=0 for at least one c c between −2-2 and 11\newline(B) f(c)=0 f(c)=0 for at least one c c between 33 and 66\newline(C) f(c)=4 f(c)=4 for at least one c c between −2-2 and 11\newline(D) f(c)=4 f(c)=4 for at least one c c between 33 and 66
Get tutor helpright-arrow

Posted 9 months ago

Question
Let f f be a continuous function on the closed interval [−5,0] [-5,0] , where f(−5)=0 f(-5)=0 and f(0)=5 f(0)=5 .\newlineWhich of the following is guaranteed by the Intermediate Value Theorem?\newlineChoose 11 answer:\newline(A) f(c)=−2 f(c)=-2 for at least one c c between −5-5 and 00\newline(B) f(c)=2 f(c)=2 for at least one c c between 00 and 55\newline(C) f(c)=2 f(c)=2 for at least one c c between −5-5 and 00\newline(D) f(c)=−2 f(c)=-2 for at least one c c between 00 and 55
Get tutor helpright-arrow

Posted 9 months ago

Question
Let f f be a continuous function on the closed interval [1,5] [1,5] , where f(1)=1 f(1)=1 and f(5)=−3 f(5)=-3 .\newlineWhich of the following is guaranteed by the Intermediate Value Theorem?\newlineChoose 11 answer:\newline(A) f(c)=2 f(c)=2 for at least one c c between 11 and 55\newline(B) f(c)=−2 f(c)=-2 for at least one c c between −3-3 and 11\newline(C) f(c)=−2 f(c)=-2 for at least one c c between 11 and 55\newline(D) f(c)=2 f(c)=2 for at least one c c between −3-3 and 11
Get tutor helpright-arrow

Posted 9 months ago

Question
Let h(x)=1x h(x)=\frac{1}{x} .\newlineCan we use the intermediate value theorem to say the equation h(x)=0.5 h(x)=0.5 has a solution where −1≤x≤1 -1 \leq x \leq 1 ?\newlineChoose 11 answer:\newline(A) No, since the function is not continuous on that interval.\newline(B) No, since 00.55 is not between h(−1) h(-1) and h(1) h(1) .\newline(C) Yes, both conditions for using the intermediate value theorem have been met.
Get tutor helpright-arrow

Posted 9 months ago

Question
Let h h be a continuous function on the closed interval [0,4] [0,4] , where h(0)=2 h(0)=2 and h(4)=−2 h(4)=-2 .\newlineWhich of the following is guaranteed by the Intermediate Value Theorem?\newlineChoose 11 answer:\newline(A) h(c)=3 h(c)=3 for at least one c c between 00 and 44\newline(B) h(c)=−1 h(c)=-1 for at least one c c between 00 and 44\newline(C) h(c)=−1 h(c)=-1 for at least one c c between −2-2 and 22\newline(D) h(c)=3 h(c)=3 for at least one c c between −2-2 and 22
Get tutor helpright-arrow

Posted 9 months ago

View all (25)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant