Question

2) xdy = (x-y) dx; y= - 3 при х = 8.

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To solve the given differential equation:

xdy = (x - y)dx

Let's separate the variables by moving all the terms involving y to one side and all the terms involving x to the other side:

xdy + ydx = xdx

Now, let's integrate both sides of the equation:

∫xdy + ∫ydx = ∫xdx

Integrating each term:

∫xdy = ∫xdx - ∫ydx

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

Now, we need to apply the initial condition y = -3 when x = 8. Substituting these values into the equation:

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

-24 = 32 - 9 + C

-24 = 23 + C

C = -47

Therefore, the solution to the given differential equation with the initial condition is:

xy = (1/2)x^2 - y^2 - 47