Purchase Solution

Using Euler's method

Not what you're looking for?

Ask Custom Question

Y'= 1/2 - (X)+2x when y(0)=1
Find the exact solution of ___ O/ <<note!!!! I don't know how to put in a zero with a line going across to make a pheee.
1a. Let h=.1 use euler & improved to approximate to get
"Phee" of .1, phee of.2, and phee of .3

Purchase this Solution
Solution Summary

This shows ho to use Euler's method to find an exact solution for a differential equation

Solution Preview

Please see attachment for response

You problem is not clear, I need to guess, I think your problem is as follows, if not, please clarify.

Problem:

y'= 1/2 - y+2x when y(0)=1
Find the exact solution of y(x)
Let h=.1 use euler & improved to appoximate to get
"Phee" of .1, phee of.2, and phee of .3

Solution:

We write equation of the form y'=-y+1/2+2x and

First we solve y'= - y

We know dy/(-y)=dx, integrate both sides to get

-ln|-y|=x+C.

Thus

-y=+e^(-x-C)=+e^(-C)e^(-x) or
-y=-e^(-x-C)=-e^(-C)e^(-x)

Thus

y=ke^(-x) for some constant k

Now we solve

y'= 1/2 - y+2x, we expect solutions to be of the form

y=f(x)(e^(-x)), for ...

Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Probability Quiz

Some questions on probability

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

View More Free Quizzes
Related BrainMass Solutions

  • The effects of the choice of step size on the Euler's approximation

    27440 Initial Value Problem (IVP); Euler's Method; Step Sizes 4. Consider the initial value problem (IVP): y'(t) = 3+t+y y(0)=1 a) Approximate y(1) using Euler's method and step sizes of 0.2. Perform these calculations by hand.

  • Euler and Modified Euler's method

    I hope this helps Thanks again Yinon The solution shows how to approximate the result of a first order ordinary differential equation using Euler's method and the modified Euler's method.

  • Differential Equations: Euler's Method

    148047 Differential Equations: Euler's Method Question: Using a computer or calculator, apply Euler's method to sketch an approximation to the solution curve for the solution to the initial-value problem. 2(d^2y)/(dt^2) + (dy)/(dt) + 4y = 0, where

  • Euler's method

    This provides an example of solving analytically and using Euler's method.

  • Numerical Euler's Method for Initial Value Problem

    27439 Numerical Euler's Method for Initial Value Problem Consider the initial value problem (IVP): y'(t) = y^2 y(0)=1 Approximate y(1) using Euler's method and step sizes of 0.25.

  • Calculus - Numerical Analysis - Approximations

    solution y(t)=t+1/(1-t) For full description of the question, please see the attached question file Solution Using Modified Euler's Method y(2.5) = 1.868164 and y(3) = 2.526854 Values from actual solution are y(2.5) = 1.833333 and

  • Numerical Methods for Differential Equations

    Using as step size h = 0.5, and fo = 1, use Euler's method to obtain f20. Your answer is an approximation to f(t10) = f(1). See the attached. The expert uses numerical methods for differential equations.

  • Euler's formula - square root of i

    31390 Euler's formula - square root of i Calculate the square root of i using a direct method and show that using Euler's formula yield the same result. See attached files.

  • Using the C++ Code to Obtain the Numerical Approx to ODE

    Using Euler's method is the simplest numerical method for approximation solving initial value ODE'S.

  • Alternative to Euler's Method Approximation

    21296 Alternative to Euler's Method Approximation Solve a Function (see attached) Explain why the Euler's method cannot be used to approximate y(2) Please see attached file The expert explains why the Euler's method cannot be used to approximate y

View More Related Solutions