Diff eq question

[lll]

http://pics.bbzzdd.com/users/mikesmith/math1.jpg

Hello. I want to solve for y(x of 2)-y(x of 1). A,B,C are constants. How can I solve this using diff equations? Thanks.

 

[magomago]

sounds like someone is having trouble in their basic math class 😉


here is a hint: you can multiply and divide the ratios to try to get anything with 'y' and 'dy' on one side, and anything with 'x' and 'dx' on the other side. If ABC are constants, they are not changing variables, and should simply follow to the side where it is the easiest to deal with them

 

[CycloWizard]

What kind of equation is it? Linear? Homogeneous? Separable? Exact?

 

[Farmer]

It's linear first order constant coefficient. The solution is going to be some exponential.

Rewriting, it is:

(dy/dx) +(1/AC) y = (B/C)

Just by inspection, the answer should be

y(x) = (H/AC) e^[-(1/AC)x] + (B/C)

Where H is some real constant depending on the boundary condition y(0). Plug it in, it works. I'm sure you could look up the proper/general solution to 1st order constant coefficient linear ODE online, but this case is simple enough to solve by inspection.

y(x of 2)-y(x of 1)

I don't understand. What is "x of 2"? What does x of something mean?

you can multiply and divide the ratios to try to get anything with 'y' and 'dy' on one side, and anything with 'x' and 'dx' on the other side.

Nah, this one is not separable.

Hope that helps/gives you the answer.

EDIT: Whoops, I didn't see the sign in front of the RHS. It's right now. Logic is still the same, just change sign in exponent. Best way to solve these is guess and check.