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baldymcgee6
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ dx }{ dt } = \frac{ 1+\sqrt{t} }{ 1+\sqrt{x} }\]

baldymcgee6
 one year ago
Best ResponseYou've already chosen the best response.0i ended up with something, but I cant explicitly solve for t

baldymcgee6
 one year ago
Best ResponseYou've already chosen the best response.0The way we were tough is to separate the variables and then integrate each side.

baldymcgee6
 one year ago
Best ResponseYou've already chosen the best response.0that's not how we were taught to do it.. http://en.wikipedia.org/wiki/Separation_of_variables

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

baldymcgee6
 one year ago
Best ResponseYou've already chosen the best response.0What chapter? It would depend what textbook. And what class.

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

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

abb0t
 one year ago
Best ResponseYou've already chosen the best response.0:O I think it is separable!

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

oldrin.bataku
 one year ago
Best ResponseYou've already chosen the best response.1This 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.

baldymcgee6
 one year ago
Best 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

oldrin.bataku
 one year ago
Best ResponseYou've already chosen the best response.1I *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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