A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
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?
anonymous
 5 years ago
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?

This Question is Closed

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.0integrate both sides \[y = \int\limits_{}^{}(x+2)\sin(x) dx = \int\limits_{}^{}x*\sin(x) +2\sin(x) dx\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{dy}{dx}=(x+2)\sin(x); y(0)=3\] \[\int\limits dy=\int\limits (x+2)\sin(x)dx\] 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: \[y(0)=3=(0)\cos(0)+\sin(0)2\cos(0)+C \implies 3=2+C \implies C=5\] \[y(x)=x \cos(x)+\sin(x)2\cos(x)+5\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay I get it; thanks.
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.