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

Denebel

Solve the initial value problem. Confirm your answer by checking that it conforms to the slope field of the differential equation. dy/dx=(x+2)sin x and y=3 when x=0 I'm not sure what this problem is asking or how to solve it?

  • 2 years ago
  • 2 years ago

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

    integrate both sides \[y = \int\limits_{}^{}(x+2)\sin(x) dx = \int\limits_{}^{}x*\sin(x) +2\sin(x) dx\]

    • 2 years ago
  2. malevolence19
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\frac{dy}{dx}=(x+2)\sin(x); y(0)=3\] \[\int\limits dy=\int\limits (x+2)\sin(x)dx\] Now it comes down to integration: \[y(x)=\int\limits x sin(x)dx+2 \int\limits \sin(x)dx\] Doing the first one using IBP you get: \[u=x; du=dx; dv=\sin(x)dx; v=-\cos(x)\] \[\int\limits x \sin(x)dx=-xcos(x)+\int\limits \cos(x)dx=-x \cos(x)+\sin(x)+C\] So we get: \[y(x)=-x \cos(x)+\sin(x)-2\cos(x)+C\] Solving the initial value we get: \[y(0)=3=-(0)\cos(0)+\sin(0)-2\cos(0)+C \implies 3=-2+C \implies C=5\] \[y(x)=-x \cos(x)+\sin(x)-2\cos(x)+5\]

    • 2 years ago
  3. Denebel
    Best Response
    You've already chosen the best response.
    Medals 1

    Okay I get it; thanks.

    • 2 years 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.