can this differential equation be solved using separation of variables?\n\frac{dy}{dx}=10 - 2y+9x\nchoose 1…

can this differential equation be solved using separation of variables?\n\frac{dy}{dx}=10 - 2y+9x\nchoose 1 answer:\na yes\nb no

can this differential equation be solved using separation of variables?\n\frac{dy}{dx}=10 - 2y+9x\nchoose 1 answer:\na yes\nb no

Answer

Explanation:

Step1: Recall separation - of - variables condition

Separation of variables requires the differential equation $\frac{dy}{dx}=f(x)g(y)$.

Step2: Analyze given equation

The given equation $\frac{dy}{dx}=10 - 2y+9x$ cannot be written in the form $\frac{dy}{dx}=f(x)g(y)$ since the right - hand side has a sum of terms involving $x$ and $y$ that cannot be factored into a product of a function of $x$ and a function of $y$.

Answer:

B. No