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

1. anonymous

$\frac{ dx }{ dt } = \frac{ 1+\sqrt{t} }{ 1+\sqrt{x} }$

2. anonymous

i ended up with something, but I cant explicitly solve for t

3. anonymous

The way we were tough is to separate the variables and then integrate each side.

4. anonymous

taught*

5. anonymous

that's not how we were taught to do it.. http://en.wikipedia.org/wiki/Separation_of_variables

6. ksaimouli

hmm sorry i have not yet learned those so sorry what chapter is this

7. anonymous

What chapter? It would depend what textbook. And what class.

8. ksaimouli

i mean name of the chapter

9. anonymous

its on ODE's

10. ksaimouli

is this college calculus

11. anonymous

yeah calc 2

12. ksaimouli

okay

13. anonymous

It's separable, no?

14. abb0t

:O I think it is separable!

15. anonymous

Multiply both sides by $$1+\sqrt{x}$$. Integrate with respect to $$t$$.

16. 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})\ dtNow, 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.

17. anonymous

@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

18. 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