Rewrite each equation as and .
Each of those is first-order linear, so solve each using the integrating factor method.
Hey, for this System I want to find the general solution but and both have constants which I can't remember how to deal with.
Find the general solution to:
And I have a non-linear system that needs to be linearised but my working is getting me nowhere.
Linearise the system around the critical point (0,0):
Any help would be greatly appreciated.
I get and - remember that when you multiply by the integrating factor, you have to multiply it to BOTH sides of the equation. Also, the arbitrary constants might not be the same... And surely that's the solution to the system of DEs since you don't have any boundary conditions...
If we expand P and Q in a Taylor series at (0,0) to first order terms we get
Since (0,0) is a critical point we have that
Plugging the the appropriate partials gives
Also on the first problem are you sure it was typed correctly and is not
otherwise it is not much of a system.