Question

Нужна помощь с Дифференциальным уравнением Помогите Плиз! Как продолжить этот пример и довести его до общего и частного? С интегралами не очень( 2dy/dx=1+x²

Answer 1

2dy/dx=1+x²
2dу=dx(1+x²)
2y=x+(x^3/3)+c

Answer 2

Solving the Differential Equation 2dy/dx = 1 + x²

To solve the differential equation 2dy/dx = 1 + x², we can follow the steps of integrating both sides with respect to x. Let's proceed with the solution.

Step 1: Integrate both sides with respect to x

Integrating both sides of the equation with respect to x gives us:

∫2dy = ∫(1 + x²)dx

Step 2: Perform the integration

Integrating the right-hand side with respect to x:

``` 2y = x + (1/3)x³ + C ``` where C is the constant of integration.

Step 3: Solve for y

Finally, solving for y gives us the general solution to the differential equation:

General Solution: ``` y = (1/2)x + (1/6)x³ + C/2 ``` where C/2 represents the constant of integration.

Particular Solution: To find the particular solution, we would need additional information such as initial conditions or boundary conditions.

This completes the process of solving the given differential equation 2dy/dx = 1 + x² and obtaining both the general and particular solutions. If you have any further questions or need additional assistance, feel free to ask!