- #1

mazz1801

- 23

- 0

## 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