anonymous
  • anonymous
1st ODE !
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[x'=(x-t)^2+1\]
anonymous
  • anonymous
This thing isn't liniar any ideas ?
zepdrix
  • 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

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zepdrix
  • 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
zepdrix
  • zepdrix
Ooo goodie! I actually am getting the same as wolfram, i just didn't simplify it far enough :)
zepdrix
  • zepdrix
Able to make sense of that? It should be correct :O
anonymous
  • anonymous
thx
anonymous
  • anonymous
|dw:1436763190196:dw| Am I right @zepdrix ?
zepdrix
  • 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).
anonymous
  • anonymous
aha thx again

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