A community for students.
Here's the question you clicked on:
 0 viewing
S
 3 years ago
use separation of variables to solve differential equation :dy/dx=t/(y+1)^(1/2) , y(1)=3 ?
S
 3 years ago
use separation of variables to solve differential equation :dy/dx=t/(y+1)^(1/2) , y(1)=3 ?

This Question is Closed

.Sam.
 3 years ago
Best ResponseYou've already chosen the best response.1multiply both sides by\[\sqrt{y+1}\] Then integrate \[\frac{dy}{dx} \sqrt{y+1}\text{ = }t\] \[\sqrt{y+1}dy=tdx\] \[\int\limits_{}^{}\sqrt{y+1}dy=\int\limits_{}^{} tdx\]

S
 3 years ago
Best ResponseYou've already chosen the best response.0I got this part, but I am confused how to solve it

.Sam.
 3 years ago
Best ResponseYou've already chosen the best response.1\[\int\limits \sqrt{y+1} \, dy=\frac{2}{3} (y+1)^{3/2}\] \[\int\limits_{}^{}tdx=tx+c\]  \[\frac{2}{3} (y+1)^{3/2} =tx+c\] \[(y+1)^{3/2}=\frac{3(tx+c)}{2}\] \[y+1=(\frac{3(tx+c)}{2})^{2/3}\] \[y=(\frac{3(tx+c)}{2})^{2/3}1\]

Algebraic!
 3 years ago
Best ResponseYou've already chosen the best response.0I think it's supposed to be dy/dt ?

Algebraic!
 3 years ago
Best ResponseYou've already chosen the best response.0then it's 2/3*(y+1)^(3/2) = (t^2)/2 +C

Algebraic!
 3 years ago
Best ResponseYou've already chosen the best response.0use I.V. to find C , solve for y(t)
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.