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baldymcgee6
 3 years ago
Solve dx/dt = = (1+sqrt(t))/(1+sqrt(x))
baldymcgee6
 3 years ago
Solve dx/dt = = (1+sqrt(t))/(1+sqrt(x))

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

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

baldymcgee6
 3 years 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
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.0hmm sorry i have not yet learned those so sorry what chapter is this

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

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

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

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

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

oldrin.bataku
 3 years 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
 3 years 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
 3 years 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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