baldymcgee6
  • baldymcgee6
Solve dx/dt = = (1+sqrt(t))/(1+sqrt(x))
Mathematics
schrodinger
  • schrodinger
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baldymcgee6
  • baldymcgee6
\[\frac{ dx }{ dt } = \frac{ 1+\sqrt{t} }{ 1+\sqrt{x} }\]
baldymcgee6
  • baldymcgee6
i ended up with something, but I cant explicitly solve for t
baldymcgee6
  • baldymcgee6
The way we were tough is to separate the variables and then integrate each side.

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baldymcgee6
  • baldymcgee6
taught*
baldymcgee6
  • baldymcgee6
that's not how we were taught to do it.. http://en.wikipedia.org/wiki/Separation_of_variables
ksaimouli
  • ksaimouli
hmm sorry i have not yet learned those so sorry what chapter is this
baldymcgee6
  • baldymcgee6
What chapter? It would depend what textbook. And what class.
ksaimouli
  • ksaimouli
i mean name of the chapter
baldymcgee6
  • baldymcgee6
its on ODE's
ksaimouli
  • ksaimouli
is this college calculus
baldymcgee6
  • baldymcgee6
yeah calc 2
ksaimouli
  • ksaimouli
okay
anonymous
  • anonymous
It's separable, no?
abb0t
  • abb0t
:O I think it is separable!
anonymous
  • anonymous
Multiply both sides by \(1+\sqrt{x}\). Integrate with respect to \(t\).
anonymous
  • anonymous
This is very clearly a separable first-order ordinary differential equation. We can easily separate as follows: $$\frac{dx}{dt}=\frac{1+\sqrt{t}}{1+\sqrt{x}}\\(1+\sqrt{x})\ dx=(1+\sqrt{t})\ dt$$Now, it should be clear that we integrate both sides.$$\int(1+\sqrt{x})\ dx=\int(1+\sqrt{t})\ dt\\x+\frac23x^\frac32=t+\frac23t^\frac32+C$$ This yields an implicit solution; for an explicit one, you'll need to isolate \(x\)... it won't be pretty.
baldymcgee6
  • baldymcgee6
@oldrin.bataku thanks for the reply, that is the same thing I did, but I couldn't figure out how to get an explicit solution. I suppose I will leave it at this. Thank you
anonymous
  • anonymous
I *highly* doubt your teacher wants an explicit solution ;-) http://www.wolframalpha.com/input/?i=solve+x+%2B+2%2F3+x%5E%283%2F2%29+%3D+t+%2B+2%2F3+t%5E%283%2F2%29%2Bc

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