Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

cander3

  • one year ago

If dy/dx=2xy and y(0)=1. What is y(1) equal to?

  • This Question is Closed
  1. FibonacciChick666
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So, this looks more like partial derivatives. That is How I shall approach it. We have: \[\frac{\delta~y}{\delta~x}=2xy\] To this we have taken the derivative WRT x. So the y terms are considered constant. If we integrate WRT x we should arrive at our initial function. So: \[ \int 2xy~ \delta x= x^2y+f(y)\] Now in order to determine f(y) we must look at our givens. So if y=0 then f(x,y)=1 so we know that f(y) must equal 1 at y(0) (because x^2y=0). So we can infer that f(y) is actually just 1. This yields the eq. \[f(x,y)=x^{2} y+1\] From here it is a plug and chug.

  2. druminjosh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    looks like a seperable ordinary differential equation to me. first solve for the equation. \[\frac{ dy }{ dx }=2xy\] if I write dy/dx as y', and divide both sides by y then we get. \[\frac{ y' }{ y }=2x\]Integrate both sides with respect to x gives: \[\ln \left| y \right|=x^{2}+C\] Therefore \[y=Ce ^{x ^{2}}\] is a solution. if y(0) = 1 then substitute this to solve for C \[1=Ce ^{0^{2}}\] so C=1 and \[y=e ^{x ^{2}}\] is the particular solution to the equation. If you substitute 1 for x into the equation, you get y(1) = e

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

    • Attachments:

Ask your own question

Ask a Question
Find 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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.