baldymcgee6
  • baldymcgee6
Solve dx/dt = = (1+sqrt(t))/(1+sqrt(x))
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.