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

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

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Intermediate Value Theoremright chevron icon

Full solution

Q. Can this differential equation be solved using separation of variables?\newlinedydx=sin⁡(3x−y) \frac{d y}{d x}=\sin (3 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 g(y) dy=h(x) dxg(y)\,dy = h(x)\,dx, where g(y)g(y) is a function of yy only and h(x)h(x) is a function of xx only.
  2. Rearrange Terms: The given differential equation is (dydx=sin⁡(3x−y))(\frac{dy}{dx} = \sin(3x - y)). We attempt to separate the variables by moving all terms involving yy to one side and all terms involving xx to the other side.
  3. Isolate Sine Function: We try to isolate sin⁡(3x−y)\sin(3x - y) to one side, but since sin⁡(3x−y)\sin(3x - y) is not a product of a function of xx and a function of yy, we cannot directly separate the variables.
  4. Unable to Separate Variables: The equation involves a sine function of a combination of xx and yy, which cannot be easily separated into a product of individual functions of xx and yy. Therefore, the equation cannot be solved using the method of separation of variables in its current form.

More problems from Intermediate Value Theorem

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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
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