Initial Value Problem. I'm really confused just need some help

[mazz1801]

Homework Statement

Solve the following Initial Value problem for x(t) and give the value of x(1)

Homework Equations

(dx/dt)-xt=-t , x(0)=2

The Attempt at a Solution

(dx/dt)-xt = -t
(dx/dt) = xt-t
(dx/dt) = t(x-1)
(1/(x-1)) (dx/dt) = t
(1/(x-1)) dx = t dt

Then I integrate both sides.

∫(1/(x-1)) dx = ∫t dt
ln[x-1] + C = (1/2)t^2

I put x=2 and t=0
ln[1] + C = (1/2)(0)^2
0 + C = 0
C = 0

So my problem is the x(1) bit... I don't know where to go with this... would I just make t=1 and solve for x and give a numerical answer by subbing i back in?
Or am I way of the mark and have everything wrong :O

 

[tiny-tim]

welcome to pf!

hi mazz1801! welcome to pf!

(try using the X² button just above the Reply box )

ln[x-1] + C = (1/2)t^2
…
C = 0
…
So my problem is the x(1) bit... I don't know where to go with this... would I just make t=1 and solve for x and give a numerical answer by subbing i back in?

("subbing i"? )

yes, that's fine

you should now get rid of the ln by writing x-1 = e^t2/2

then put t = 1

 

[mazz1801]

Thank you very much tiny-tim :)