How to integrate a function

[Goosemaster]

Originally posted by: Howard

Originally posted by: Goosemaster

Originally posted by: Howard
dy/dx + P(x)y = g(x) is the general form of a first-order linear diff eq.

good. I needed to know if you knew that.

Couldn't you see I had already gotten that far in my work?

you divided by x^2..that means nothing....a calc student could've done that...but you are on the right track....


i'll be back in 5..I have go to move my car

 

[DrPizza]

I see that you put it in that form...
If you're using the method of integrating factors, then you wind up with
u = e^int(p(x)dx)
so,
e^ (integral of 1 + 2/x)
= e^(x +2lnx)
= e^x * e^ln(x^2)
= e^x * x^2
=x^2 e^x = integrating factor

 

[DrPizza]

oh, so you end up integrating x^2 e^x * (e^x / x^2)

don't you end up with the integral of e^2x??
I didn't end up with an x in the denominator 🙂

 

[Howard]

Originally posted by: DrPizza
I see that you put it in that form...
If you're using the method of integrating factors, then you wind up with
u = e^int(p(x)dx)
so,
e^ (integral of 1 + 2/x)
= e^(x +2lnx)
= e^x * e^ln(x^2)
= e^x * x^2
=x^2 e^x = integrating factor

Ah, I'd forgotten my logarithm rules.

 

[DrPizza]

Did I make any errors? I only teach that about once every three years, so I'm pretty rusty at it.

 

[DrPizza]

Originally posted by: Howard

Originally posted by: DrPizza
I see that you put it in that form...
If you're using the method of integrating factors, then you wind up with
u = e^int(p(x)dx)
so,
e^ (integral of 1 + 2/x)
= e^(x +2lnx)
= e^x * e^ln(x^2)
= e^x * x^2
=x^2 e^x = integrating factor

Ah, I'd forgotten my logarithm rules.

Damn you! I've gone through 5 pages of scratch work trying to figure out how to integrate e^2x / x. All because you forgot your logarithm rules 🙂 😛

Oh well, I won't have to review integrating factors for myself again this year.

 

[Howard]

😀

Good practice, no? So is the function impossible to integrate, like e^x^2?

 

[jessicak]

haha we have that exact same question in my diffeq book. Do you use the Advanced Engineering Mathematics book by Zill?

 

[Howard]

No, but the author is the same.

 

[Goosemaster]

LOL....the entire tiime I had ignoring that fact that it was a diff eqtn at the top and you were soling it HAHAHAHA

I simply looked at the bottom part and continued...lol