Solve y''-4=0: Find Function for y'=0, y=1 when x=2

[dontdisturbmycircles]

Homework Statement

If y'=0 and y=1 when x=2, and y''-4=0, find the function.

Homework Equations

$$\frac{dy}{dx}=\int\frac{d^{2}y}{dx^{2}}$$

The Attempt at a Solution

I hate posting this because I am pretty sure the solution is easy but I just can't seem to see through this question...

If y'=0 then there must be no x term in the function f(x)... thus y=C is the only possibility. So then y=1 is the only possibility for the initial conditions given... And if y''=4 then shouldn't y'=4x+C? :/

 

[radou]

Homework Statement

If y'=0 and y=1 when x=2, and y''-4=0, find the function.

Homework Equations

$$\frac{dy}{dx}=\int\frac{d^{2}y}{dx^{2}}$$

The Attempt at a Solution

I hate posting this because I am pretty sure the solution is easy but I just can't seem to see through this question...

If y'=0 then there must be no x term in the function f(x)... thus y=C is the only possibility. So then y=1 is the only possibility for the initial conditions given... And if y''=4 then shouldn't y'=4x+C? :/

The boundary values are y(2) = 1 and..? What do you mean by y' = 0? For which x is this true?

 

[neutrino]

Have you tried solving the equation y" - 4 =0, and then applying the initial conditions?

If y'=0 then there must be no x term in the function f(x)... thus y=C is the only possibility. So then y=1 is the only possibility for the initial conditions given...

Remember, they are not the general expression as a function of x; those are values of the function and its derivative at the point x = 2.

 

[cristo]

Homework Statement

If y'=0 and y=1 when x=2, and y''-4=0, find the function.

These intial conditions are y'(2)=0 and y(2)=1. You have assumed y'=0 for all x.

 

[dontdisturbmycircles]

Ahhh okay I was misreading the damned question, ... I kinda thought it was worded funny... Trying to breeze through my homework too fast I guess.

Sorry! Thanks all, I get it now :-)

 

[HallsofIvy]

It didn't occur to you that is y'= 0 for all x, then y" couldn't be 4!

 

[dontdisturbmycircles]

Yes I knew it was impossible as well. But I figured that the question was not written wrong, I should have reread the question more carefully but I was in too much of a hurry(was due in like 10 minutes). My appologies.