First order differentials & euler's method

In summary, the conversation is about solving a first order differential equation using Euler's method. The equation given is y' = x + y with an initial value of y(0) = 1. The person is trying to figure out the solution and has reached the step of finding the exact solution of the initial value problem. They are also discussing the accuracy of Euler's method and its relation to finding the exact solution.
  • #1
raincheck
38
0
I'm having trouble solving first order differential equations for euler's method.

right now I'm trying to figure out: y' = x + y y(0) = 1

i have: dy/dx - y = x
p(x)=-1 , q(x)=x

u=e^(-x)

y=e^x [integral](xe^-x)dx

.. i don't think I'm doing this right, where am i going wrong?

[sorry about not using the right symbols & thank you!]
 
Last edited:
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  • #2
I thought Euler's method was to do it numerically.

I have no idea.
 
  • #3
JasonRox said:
I thought Euler's method was to do it numerically.

I have no idea.

well, i guess it isn't exactly Euler's method, but it's finding the accuracy OF it, i just realized that. And to find it, I have to find the exact solution of that initial value problem..
 

What is a first-order differential?

A first-order differential is a mathematical equation that relates the rate of change of a dependent variable to the independent variable. It is called a first-order differential because it only involves the first derivative of the dependent variable.

What is Euler's method?

Euler's method is a numerical method for solving ordinary differential equations (ODEs). It involves using discrete time steps to approximate the solution of a differential equation. It is a simple and widely used method for solving ODEs.

When is Euler's method used?

Euler's method is used when the differential equation cannot be solved analytically or when the analytical solution is too complex to be useful. It is also used when the differential equation involves initial conditions that can be easily input into the numerical method.

What are the limitations of Euler's method?

Euler's method has some limitations, such as the need for small time steps to achieve accurate results. It also does not guarantee the accuracy of the solution and can produce errors, especially when used to solve stiff differential equations. It is also a first-order method, meaning that the error in the solution will decrease linearly as the time step decreases.

How is Euler's method implemented?

Euler's method is implemented by first converting the differential equation into a discrete form using the formulas for the first derivative. Then, a starting point is chosen, and the method is iteratively applied to calculate the solution at each time step. The smaller the time step, the more accurate the solution will be.

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