A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 2 years ago
If dy/dx=2xy and y(0)=1.
What is y(1) equal to?
anonymous
 2 years ago
If dy/dx=2xy and y(0)=1. What is y(1) equal to?

This Question is Closed

FibonacciChick666
 2 years ago
Best ResponseYou've already chosen the best response.0So, 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.

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0looks 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
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.