Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
Chena804
Group Title
Find the general solution of the given differential equations. Give the largest interval I over which the general solution is defined. Determine whether there are any transient terms in the general solution.
y' + 2xy = (x^3)
ydx = (y(e^y)  2x)dy
(dP)/(dt) + 2tP = P + 4t  2
 2 years ago
 2 years ago
Chena804 Group Title
Find the general solution of the given differential equations. Give the largest interval I over which the general solution is defined. Determine whether there are any transient terms in the general solution. y' + 2xy = (x^3) ydx = (y(e^y)  2x)dy (dP)/(dt) + 2tP = P + 4t  2
 2 years ago
 2 years ago

This Question is Open

hellow Group TitleBest ResponseYou've already chosen the best response.0
The last one is separable. dP/dt = P2tP + 4t2 dP/dt = P(12t) + 2(2t1) = P(12t) 2(12t) dP/dt = (P2)(12t) 1/(P2)dP = (12t)dt integrate both sides lnP2=tt^2+c This solution is defined for all P except P= 2 (since ln(0) is not defined). But we can check the solution P= 2. Plugging that into the original ODE we get 0 +2t(2)= 2+4t2 4t=4t. So P=2 also works. So, although the given solution is not defined for P=2, there is a solution when P=2. You could try integrating factors for the first problem, but there might be an easier way. I am not sure what to try for the middle problem.
 2 years ago

hellow Group TitleBest ResponseYou've already chosen the best response.0
I also realized that the middle one is linear in terms of x. You have \[y \frac{ dx }{ dy}=y e^{y}2x\] or \[y \frac{ dx }{ dy}+2x=y e^{y}\] or\[\frac{ dx }{ dy}+2x/y=e^{y}\]which is linear with respect to x and its derivatives. Thus it can be solved with integrating factors. Once you calculate your integrating factor, I think you will find it is y^2. Thus\[(xy ^{2})'=e ^{y}y ^{2}\]\[xy ^{2}=\int\limits_{}^{}e ^{y}y ^{2}dy\]\[xy ^{2}=y ^{2}e ^{y}2y e ^{y}+2e ^{y}+c\]
 one year ago

hellow Group TitleBest ResponseYou've already chosen the best response.0
The first problem can be solved in a similar way. It is linear with respect to y and its derivatives. The integration factor is e^(x^2), which means that the right hand side becomes \[\int\limits_{?}^{?}x ^{3}e ^{x ^{2}}dx\] If you let u=x^2, then the integral becomes much easier. Using the table method for inegration by parts I came up with \[x ^{2}y=1/2(x ^{2}e ^{x ^{2}}e ^{x ^{2}})+c\]
 one year ago
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
 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.