Using Euler's method
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
https://brainmass.com/math/ordinary-differential-equations/using-eulers-method-2464
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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 ...
Solution Summary
This shows ho to use Euler's method to find an exact solution for a differential equation