Critical Points and Differential Equations Helppp

[vinverth]

Critical Points and Differential Equations! Helppp

Hello everyone..Find it embarrassing enough on asking a question on my very first post but I've been an avid reader of the forums for the past couple of months and been finding what i need for all my assignments here.So a big Thank You to all who've helped.I'm A EE grad and have a math course in my final semester so am a complete noob when it comes to grad math courses,a little consideration here while posting replies or even answers.So here i have a couple of q's whose answers or at least a decent start I've been searching all over the web.

1.Find the differential equations for the polar functions r,ө of the following two-dimensional systems.

(a) x'=x+y
y'=x-y

2.Locate the critical points of the following systems.

(a) x'=x-y²
y'=x²-y²
These are both separate questions.Answers to anyone pleasezzz..
(b) x'=sin(y)
y'=cos(x)


Thank You again to everyone and please bail me out guys!

 

[HallsofIvy]

Hello everyone..Find it embarrassing enough on asking a question on my very first post but I've been an avid reader of the forums for the past couple of months and been finding what i need for all my assignments here.So a big Thank You to all who've helped.I'm A EE grad and have a math course in my final semester so am a complete noob when it comes to grad math courses,a little consideration here while posting replies or even answers.So here i have a couple of q's whose answers or at least a decent start I've been searching all over the web.

1.Find the differential equations for the polar functions r,ө of the following two-dimensional systems.

(a) x'=x+y
y'=x-y

In polar coordinates, $x= r cos(\theta)$ and $y= r sin(\theta)$. from that $x'= r' cos(\theta)- r sin(\theta)\theta'$ and $y'= r' sin(\theta)+ r cos(\theta)\theta'$.

2.Locate the critical points of the following systems.

(a) x'=x-y²
y'=x²-y²
These are both separate questions.Answers to anyone pleasezzz..

"Critical points" are where the derivatives are both 0. solve $x- y^2= 0$, $x^2- y^2= 0$. There are 3 critical points.

(b) x'=sin(y)
y'=cos(x)


Thank You again to everyone and please bail me out guys!