Question

Solve dx/dt = = (1+sqrt(t))/(1+sqrt(x))

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

taught*

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

i mean name of the chapter

Answer 9

its on ODE's

Answer 10

is this college calculus

Answer 11

yeah calc 2

Answer 12

okay

Answer 13

It's separable, no?

Answer 14

:O
I think it is separable!

Answer 15

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

Answer 16

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.

Answer 17

@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

Answer 18

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