A community for students.
Here's the question you clicked on:
 0 viewing
alyannahere
 2 years ago
hi ! can you help me solve this ?
Find the general or particular solution for this differential equation
1. dy/dt=2y
2. dy/dx = 0.5y; y(0) = 100
i realized that it's all y so i don't really know how to go about that.
alyannahere
 2 years ago
hi ! can you help me solve this ? Find the general or particular solution for this differential equation 1. dy/dt=2y 2. dy/dx = 0.5y; y(0) = 100 i realized that it's all y so i don't really know how to go about that.

This Question is Closed

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.0First one :) \[\huge \frac{dy}{dt}=2y\] Let's multiply both sides by dt, and divide both sides by 2y

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.0\[\huge \frac{dy}{2y}=dt\] Now integrate both sides :)

alyannahere
 2 years ago
Best ResponseYou've already chosen the best response.0not really sure how.. ?

alyannahere
 2 years ago
Best ResponseYou've already chosen the best response.0i'm really sorry.. i don't know how to go about this problem @PeterPan

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.0Well, maybe if it's tweaked a bit, you'll find it simpler... \[\huge \frac{1}{2}\int\limits\frac{dy}{y}=\int\limits dt\] Sorry about the other one, it's a typo o.O

alyannahere
 2 years ago
Best ResponseYou've already chosen the best response.0so that is 1/2 1/y = C ?

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.0No... remember \[\huge \int\limits \frac{dx}{x}=\ln(x) + C\]

alyannahere
 2 years ago
Best ResponseYou've already chosen the best response.0so it's 1/2 ln y = C ?

alyannahere
 2 years ago
Best ResponseYou've already chosen the best response.0my friend said the answer is y=C e ^2t

alyannahere
 2 years ago
Best ResponseYou've already chosen the best response.0i don't know how he got it

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.0Hang on, just integrate for now, and tell me what you got :)\[\huge \frac{1}{2}\int\limits\frac{dy}{y}=\int\limits dt\]

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.0Well, isn't it though \[\huge \int\limits dx = x + C\]

alyannahere
 2 years ago
Best ResponseYou've already chosen the best response.0how did it become dx ? i'm so sorry i just really don't understand this lesson

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.0This is just a reminder :) The integral of 1 is just x (plus a constant)

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.0Then... What's \[\huge \int\limits dt\]

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.0Very good :) So now, the result of \[\huge \frac{1}{2}\int\limits\frac{dy}{y}=\int\limits dt\] is...?

alyannahere
 2 years ago
Best ResponseYou've already chosen the best response.0wait question, why is did you put 2y in the denominator in the first place?

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.0Well, because we want to put everything involving y with the dy and everything involving t with the dt

alyannahere
 2 years ago
Best ResponseYou've already chosen the best response.0that makes sense... but was my answer correct ?

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah :) But we're not yet done, hang on

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.0let's \[\huge \frac{1}{2}\ln(y)=t+C\]playing with it a bit... \[\huge \ln(y) = 2t + 2C\]

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.0But 2C is just another constant, so we can disregard the coefficient ln(y) = 2t + C Getting it so far?

alyannahere
 2 years ago
Best ResponseYou've already chosen the best response.0oh then you put e to both sides to get sid of the ln ?

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.0That's right :) and e^C is again, just another constant, so just replace it with C And you're done :)

alyannahere
 2 years ago
Best ResponseYou've already chosen the best response.0how come it's addition and not multiplication ?

alyannahere
 2 years ago
Best ResponseYou've already chosen the best response.0y=C e ^2t ? that's the answer..

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.0Actually, it's \[\huge y = e^{2t + C}\] right? By laws of exponents, this is just \[\huge y = e^Ce^{2t}\] And once again, I said e^C is just another constant anyway, so you can just replace it with C. :)

alyannahere
 2 years ago
Best ResponseYou've already chosen the best response.0ohhh !!! i see... thank you sooo much !!!!!!!!!
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.