Consider the differential equation dy/dx = (y-1)^2 cos(Πx)

• gonzalo12345
In summary, the conversation discusses a differential equation and solving for a particular solution with an initial condition. Option (a) suggests plugging in y=c to the equation and using the initial condition to find the value of c. Option (b) suggests multiplying each side by dx/(y-1)^2 and integrating directly, using the initial condition as integration limits or finding the integration constant. The conversation ends with a reminder to have a strong understanding of basics and a reference to a helpful blog post.
gonzalo12345
HW help!

Homework Statement

consider the differential equation dy/dx = (y-1)^2 cos(Πx)

a.There is a horizontal line with y =c that satisfies this equation. Find the value of c
b. Find the particular solution y =f(x) tot the differential equation with the initial condition f(1) = 0

n/a

The Attempt at a Solution

I tried to do the problem, but I can't separate the y variables from the x, help!

(a) What happens when you plug y=c to the differential equation? You should get just an equation depending on c (and x, but if you restrict x, you can divide it out).
(b) Try multiplying each side by dx/(y-1)^2 and integrating directly. Then, you can either use your initial conditions as your integration limits or plug them into find your integration constant.

I got it, I got c=1 thanks

While it is, in fact, almost trivial to separate x and y ((y-1)2 and cos($\pi$), in effect, are separated- they are multiplied), you don't have to find the general solution to answer (b)!

i don't know much but i do know that u need to get your basics right. come see the lastest post in my blog. the web link may be of help

1. What is a differential equation?

A differential equation is a mathematical equation that relates a function with its derivatives. It represents how a function changes over time or space and is commonly used in scientific and engineering fields to model real-world phenomena.

2. What is the solution to the given differential equation?

The solution to this differential equation is y(x) = tan(πx - π/2) + 1.

3. How do you solve a differential equation?

There is no one specific method for solving a differential equation. It depends on the type of equation and its complexity. Generally, one can use techniques such as separation of variables, substitution, or using integrating factors to solve a differential equation.

4. What is the role of the constant of integration in solving a differential equation?

The constant of integration is a constant that is added to the general solution of a differential equation. It accounts for any additional unknown factors or initial conditions that may affect the solution.

5. Can the given differential equation be solved using numerical methods?

Yes, this differential equation can be solved using numerical methods such as Euler's method or Runge-Kutta methods. These methods use numerical approximations to find an approximate solution to the differential equation.

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