Verifying phi(x) is an explicit solutionDomain = RInterval: x>=-2

[joeseppe]

Just started Engineering Math III and have a question. Sorry about the notation, our library computers have scripts disabled.

My math prof does a poor job of explaining the concepts. Help me out!

Homework Statement

Verify the indicated function y=phi(x) is an explicit solution of the given first order DE. Proceed by considering phi simply as a function, give its domain. Then by considering phi as a solution of the DE, give at least one interval I of definition.

Homework Equations

(y-x)y'=y-x+8
y=x+4(root(x+2))

The Attempt at a Solution

I first got y'

y=x+4[(x+2)^(1/2)]
y'=2/root(x+2)

then plugged it into the original

8root(x+2) / root(x+2) = 4root(x+2) +8
8=4root(x+2)+8
0=4root(x+2)

 

[vela]

You calculated y' incorrectly. Try again.

 

[joeseppe]

You calculated y' incorrectly. Try again.

y'=1=[2/root(x+2)]

Then I plugged it into the original and got both sides to equal.

BUT
I still have no idea what the original question is actually asking me to do in each part?

 

[vela]

The first thing you're being asked for is the domain of the function $\phi(x)=x+4\sqrt{x+2}$. The solution to a differential equation, however, is valid on some interval, which isn't necessarily the same as the domain of the solution. The question is asking you for this interval as well.

It's probably easiest to understand the difference by seeing specific examples, so you may find the following page helpful:

http://tutorial.math.lamar.edu/Classes/DE/IoV.aspx