Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

chambek Group Title

dy/dx+3y=7 y(0)=0 Find a particular solution to the nonhomogeneous differential equation.

  • one year ago
  • one year ago

  • This Question is Closed
  1. chambek Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Also.....Find the solution to the initial value problem. I'm trying to learn this on my own but really am just not getting it.

    • one year ago
  2. UnkleRhaukus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\frac{\mathrm dy}{\mathrm dx}+3y=7\] is a linear equation of the from \[\frac{\mathrm dy}{\mathrm dx}+p(x)y=q(x)\] to solve the linear equation we need an integrating factor \[\mu(x)=e^{\int p(x)\text dx}\] then \[\frac{\mathrm d}{\mathrm dx}\big(\mu(x)y\big)=\mu(x) q(x)\]\[\mu(x)y=\int{\mu(x) q(x)\text dx} \] \[y=\quad\dots\]

    • one year ago
  3. UnkleRhaukus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    after integration you will have a constant of integration, substituting the initial value will allow you to find it

    • one year ago
  4. chambek Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I got the first part! Thanks, I'm trying to get the part with the initial value now....where do i substitute that in?

    • one year ago
  5. UnkleRhaukus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    y = y(x) the condition is y(0) = 0 which means (x,y) = (0,0) is a solution

    • one year ago
  6. chambek Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok....doing that I got 0....and that was wrong, it is asking for a y=..... I'm sorry i dont understand my professor at all so i essentially now nothing about diffe q's

    • one year ago
  7. chambek Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    or grammar apparently....

    • one year ago
  8. UnkleRhaukus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    can you show some working

    • one year ago
  9. chambek Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    sure, so i got (7/3) as the particular solution to the nonhomogeneous equation. then going from there, I included a C in my integral so I could plug in 0 for y and solce for c, then get an equation for y=.... \[3y=7+C\] I found C to be -7 at y(0)=0 giving me \[3y=7-7\] which just doesnt really make too much sense, but I tried 0 regardless and realized I have no clue what I'm doing haha

    • one year ago
  10. chambek Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    oh no wait a second....hold on

    • one year ago
  11. chambek Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    grrr nevermind, that still got me 0, I had made a mistake in my algebra......

    • one year ago
  12. UnkleRhaukus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\frac{\mathrm dy}{\mathrm dx}+3y=7\]\[\mu(x)=e^{\int 3\text dx}=e^{3\int \text dx}=e^{3x}\]\[\frac{\mathrm d}{\mathrm dx}\big(e^{3x}y\big)=7e^{3x}\] \[e^{3x}y=\int{7 e^{3x}\text dx}=7\int e^{3x}\text dx=7\frac{e^{3x}}3+c\] \[y=\frac73+ce^{-3x}\] \[y(0)=0\] \[0=\frac73+c\]\[c=-\frac73\] \[y=\frac73-\frac73e^{-3x}\]

    • one year ago
  13. chambek Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ..............so, i got that awhile ago, and I kept putting the answer in as you have it, but, the equation is in terms of t.......*facepalm* thanks for the help!

    • one year ago
    • Attachments:

See more questions >>>

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.