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baldymcgee6Best ResponseYou've already chosen the best response.0
\[\frac{ dx }{ dt } = \frac{ 1+\sqrt{t} }{ 1+\sqrt{x} }\]
 one year ago

baldymcgee6Best ResponseYou've already chosen the best response.0
i ended up with something, but I cant explicitly solve for t
 one year ago

baldymcgee6Best ResponseYou've already chosen the best response.0
The way we were tough is to separate the variables and then integrate each side.
 one year ago

baldymcgee6Best ResponseYou've already chosen the best response.0
that's not how we were taught to do it.. http://en.wikipedia.org/wiki/Separation_of_variables
 one year ago

ksaimouliBest ResponseYou've already chosen the best response.0
hmm sorry i have not yet learned those so sorry what chapter is this
 one year ago

baldymcgee6Best ResponseYou've already chosen the best response.0
What chapter? It would depend what textbook. And what class.
 one year ago

ksaimouliBest ResponseYou've already chosen the best response.0
i mean name of the chapter
 one year ago

ksaimouliBest ResponseYou've already chosen the best response.0
is this college calculus
 one year ago

abb0tBest ResponseYou've already chosen the best response.0
:O I think it is separable!
 one year ago

wioBest ResponseYou've already chosen the best response.1
Multiply both sides by \(1+\sqrt{x}\). Integrate with respect to \(t\).
 one year ago

oldrin.batakuBest ResponseYou've already chosen the best response.1
This is very clearly a separable firstorder 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.
 one year ago

baldymcgee6Best ResponseYou've already chosen the best response.0
@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
 one year ago

oldrin.batakuBest ResponseYou've already chosen the best response.1
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
 one year ago
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