## anonymous one year ago 1st ODE !

1. anonymous

$x'=(x-t)^2+1$

2. anonymous

This thing isn't liniar any ideas ?

3. zepdrix

Hmm I have an idea.. but it's not giving me the same solution as Wolfram.. So I'm thinking I made a boo boo somewhere. I'll at least show you my attempt

4. zepdrix

Let $$\large\rm u=x-t$$ Differentiating our sub with respect to time gives $$\large\rm u'=x'-1\qquad\to\qquad x'=u'+1$$ Subbing everything in gives us,$\large\rm u'+1=(u)^2+1$$\large\rm u'=u^2$And then just seperation, ya? :o

5. zepdrix

Ooo goodie! I actually am getting the same as wolfram, i just didn't simplify it far enough :)

6. zepdrix

Able to make sense of that? It should be correct :O

7. anonymous

thx

8. anonymous

|dw:1436763190196:dw| Am I right @zepdrix ?

9. zepdrix

A little hard to read that last line. Lemme just make a note that you should be careful to include your constant of integration at this step.$\large\rm -\frac{1}{u}=t+c$Put the negative on the other side,$\large\rm \frac{1}{u}=c-t$Solving for u,$\large\rm \frac{1}{c-t}=u$Then you need to undo your substitution. Remember, we're trying to solve for x(t).

10. anonymous

aha thx again