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Can this differential equation be solved using separation of variables? (dy)/(dx)=xy+5x Choose 1 answer: (A) Yes (B) No

Can this differential equation be solved using separation of variables?\newlinedydx=xy+5x \frac{d y}{d x}=x y+5 x \newlineChoose 11 answer:\newline(A) Yes\newline(B) No

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Full solution

Q. Can this differential equation be solved using separation of variables?\newlinedydx=xy+5x \frac{d y}{d x}=x y+5 x \newlineChoose 11 answer:\newline(A) Yes\newline(B) No
  1. Identify Differential Equation: Identify the differential equation.\newlineThe given differential equation is dydx=xy+5x\frac{dy}{dx} = xy + 5x.
  2. Check Equation Form: Check if the equation can be written in the form of a product of a function of xx and a function of yy. The right-hand side of the equation, xy+5xxy + 5x, cannot be expressed as a product of a function of xx and a function of yy because the term 5x5x does not contain yy.
  3. Determine Separation Feasibility: Determine if separation of variables is possible. Separation of variables requires that the equation can be written in the form dydx=g(y)⋅h(x)\frac{dy}{dx} = g(y) \cdot h(x), where g(y)g(y) is a function of yy only and h(x)h(x) is a function of xx only. Since the term 5x5x cannot be separated into a function of yy, separation of variables is not possible for this differential equation.

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