Question

Y'+2x-3=0 !!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

Решение системы графическим способом

Answer 2

It seems like you've provided a first-order ordinary differential equation (ODE) in its general form:

$\frac{dy}{dx} + 2x - 3 = 0$

To solve this ODE and find the function $y(x)$, we need to separate the variables and then integrate both sides.

Step 1: Separate variables

Move the terms involving $y$ to one side and the terms involving $x$ to the other side:

$\frac{dy}{dx} = 3 - 2x$

Step 2: Integrate both sides

Now, integrate both sides with respect to $x$:

$\int \frac{dy}{dx} dx = \int (3 - 2x) dx$

$\int dy = \int (3 - 2x) dx$

Step 3: Perform the integration

Integrate both sides:

$y = \int (3 - 2x) dx$

To integrate $3$ with respect to $x$, we get:

$\int 3 dx = 3x + C_1$

To integrate $-2x$ with respect to $x$, we get:

$\int -2x dx = -x^2 + C_2$

where $C_1$ and $C_2$ are constants of integration.

Step 4: Final Solution

Now, combining the results from the integration:

$y = 3x - x^2 + C$

where $C = C_1 + C_2$ is the combined constant of integration.

So, the general solution to the given first-order ODE is:

$y(x) = 3x - x^2 + C$

Each specific value of $C$ will give you a different particular solution to the differential equation. To find the particular solution that satisfies specific initial or boundary conditions, you need additional information about the problem.