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)=2sin(x)-3cos(y) Choose 1 answer: (A) Yes (B) No

Can this differential equation be solved using separation of variables?\newlinedydx=2sin⁡(x)−3cos⁡(y) \frac{d y}{d x}=2 \sin (x)-3 \cos (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=2sin⁡(x)−3cos⁡(y) \frac{d y}{d x}=2 \sin (x)-3 \cos (y) \newlineChoose 11 answer:\newline(A) Yes\newline(B) No
  1. Check Equation Form: To determine if the given differential equation can be solved using separation of variables, we need to see if we can express the equation in the form of a product of a function of xx and a function of yy, such that we can integrate both sides separately. Let's try to rearrange the equation.
  2. Separate Variables Attempt: We start by trying to separate the variables yy and xx on different sides of the equation. We want to get all the yy terms on one side and all the xx terms on the other side. We can attempt to do this by dividing both sides by −3cos⁡(y)-3\cos(y) and multiplying by dxdx to get dydy on one side.
  3. Variable Separation Failure: After attempting to separate the variables, we would have:\newlinedy−3cos⁡(y)=2sin⁡(x)−3cos⁡(y)dx\frac{dy}{-3\cos(y)} = \frac{2\sin(x)}{-3\cos(y)}dx\newlineHowever, we notice that the right side of the equation still contains both xx and yy, which means we cannot separate the variables as required for the method of separation of variables.
  4. Conclusion: Since we cannot express the equation in a form where each side contains only one variable and its differentials, the differential equation cannot be solved using 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