Question

2) xdy = (x-y) dx; y= - 3 при х = 8.

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To solve the given differential equation, we can separate the variables and integrate both sides. Here's the solution:

Given: xdy = (x - y)dx

Let's rewrite the equation as:

xdy + ydx = xdx - ydx

Now, integrate both sides:

∫xdy + ∫ydx = ∫xdx - ∫ydx

Integrating each term:

xy + ∫ydx = (1/2)x^2 - ∫ydx

xy + yx = (1/2)x^2 - yx + C

2yx = (1/2)x^2 + C

Since we have a specific condition, y = -3 when x = 8, we can substitute these values into the equation:

2(-3)(8) = (1/2)(8^2) + C

-48 = 32 + C

C = -48 - 32

C = -80

Therefore, the particular solution to the given differential equation with the condition y = -3 when x = 8 is:

2yx = (1/2)x^2 - 80