A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
GENERAL SOLUTION
y'=3(y+1) ANS: y=ce^3x1
anonymous
 one year ago
GENERAL SOLUTION y'=3(y+1) ANS: y=ce^3x1

This Question is Closed

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0The question is: given the differential equation, find the general solution?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0Or are you supposed to test the equation to see if its true?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0to test the equation to see if its true

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0OK, we want to plug it into the differential equation y' = 3(y + 1) and check that both sides are equal. We already know that what y equals, so we can evaluate the righthand side (RHS) of the equation: RHS 3(y + 1) = 3([ce^{3x} 1] + 1) = 3(ce^{3x}) = 3ce^{3x}.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0Is this the same as the lefthand side (LHS)? Well, we need to find the value of y' We can just take the derivative of our given y to find this. See what you get. :)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0OK, can you take the derivative of y?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0I think this question means we need to verify that the answer is y=e^{3x}1 using ode techniques. use separation of variables

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0I'm straining my memory now as its been a long time. I think this a first order linear equation dy/dx  3y = 3

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0Integrating factor = e ^ [INT 3dx) = e^3x next you multiply each term in the equation by this integrating factor

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0I'll have to refresh my memory on this stuff....

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0yeah we can use integrating factor Actually there is more than one method to solving this equation and it should lead to the same answer.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0either separation of variables or integrating factor works... However, separation of variables seems to be the fastest way to retrieve the solution

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0e^3x * dy/dx  3y e^3x = 3 e^3x y e^3x = INT 3 3x dx

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0y e^3x = e^3x + C

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0now we divide by e^3x y = 1 + C / e^3x not sure about that!

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0that gives y = ce^3x + 1 different sign!!???

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0maybe it's a typo? I'll do the separation of variables way and pm you what I got @welshfella

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0i might have gone wrong somewhere...

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0 its about 50 years since I last did these lol

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0oh I see now i made an error right at the beginning its dy/dx  3y = 3 ( not 3)

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0it is 1 not 1 y = ce^3x  1

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0yup and also you have to take that minus sign into consideration. so your p(x) for integrating factor is 3

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1How about try substitution: with p=y+1 then y=p1, y'=p' y'=3(y+1) becomes p'=3(p) p'/p=3 integrate both sides log(p)=3p+C raise to power of e \(p=e^{3p+C}=Ce^{3p}\) [note the two C's have different values] Back substitute \(y+1=Ce^{3(y+1)}\) \(y=Ce^{3(y+1)}1\)

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0substitution method is a killer torture method for this problem though ...like it works but I still think that separation of variables is the fastest way to get the solution.
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.