A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
how do you do this separable equations problem: dx/dt = te^t x(0)=1
anonymous
 5 years ago
how do you do this separable equations problem: dx/dt = te^t x(0)=1

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{dx}{dt}=te^t \rightarrow dx=te^tdt \rightarrow \int\limits_{}{}dx=\int\limits_{}{}te^tdt\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{dx}{dt}=te^t \rightarrow dx=te^tdt \rightarrow \int\limits_{}{}dx=\int\limits_{}{}te^tdt\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This is just\[x=e^t(t1)+c\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0To find c, you have\[x(0)=e^0(01)+c=1 \rightarrow c=2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So your equation is\[x(t)=e^t(t1)+2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how did you get e^t(t1) is it necessary to use the product rule for that integration or what?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You will use integration by parts.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0could you show me how to do that?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I'll write it and scan  it will be quicker.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0alright thanks i'm trying it now

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Just have to wait a min, since the software for my scanner is a pain

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you think you could help me out with another one after this?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Maybe  I'm supposed to be getting ready for uni.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0alright well its dy/dx = (xy)^(1/2) and i just wasn't sure how you set that one up

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Just split the factors up using power laws.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so you would end up with dy/sqrt(y) = sqrt x dx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{dy}{dx}=(xy)^{1/2} = x^{1/2}y^{1/2} \rightarrow \frac{dy}{y^{1/2}}=x^{1/2}dx\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then after you integrate would you have 2 sqrt y = 2/3 x^(3/2)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Here's the scan for the first one.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and when it's all said and done i had \[y= (x ^{3/2}/3)^2 + (c/2)^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i feel like thats not right at all

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits{}{}\frac{dy}{y^{1/2}}=\frac{y^{1/2}}{1/2}=2y^{1/2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{}{}x^{1/2}dx = \frac{x^{3/2}}{3/2}=\frac{2}{3}x^{3/2}+c\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I added the constant then.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[2y^{1/2}=\frac{2}{3}x^{3/2}+c\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Divide by 2 to clean up:\[y^{1/2}=\frac{1}{3}x^{3/2}+c\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You don't have to write c/2 since c is just a constant  constants just keep absorbing constants since in the end, their value is determined by initial conditions and you'll end up with the same number.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ohhhh ok i think i got it since c is a constant i dont need to divide it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i really appreciate it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0there should be a link next to my name in this area we're typing in. It's a blue link that says, "Become a fan"

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Should have a 'thumbs up' icon...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it just has hero and the 110 fans

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0refresh the page...sometimes that helps

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it just has hero and the 110 fans

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah, the site's awkward

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thanks man i appreciate it
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.