# NON-LINEAR SYSTEM of DE's Help please

• March 9th 2010, 12:02 PM
RedZone231
NON-LINEAR SYSTEM of DE's Help please
Hello everyone,

I have a differential equations test coming up in a few days, and from all the questions in the book there was only one that I could not do. I am afraid the teacher will put this one on the test:

$dx/dt=x^2 +y$
$dy/dt=x^2 y^2$

Show that, for a solution (x(t),y(t)) satisfying the initial condition (x(0),y(0))=(0,1) there exists a time t* such that $x(t)-> infinity$ as $t->t*$. In other words, the solution blows up in finite time. [Hint: dy/dt is greater or equal 0 for all x and y]

Since this problem was in the chapter about Uniqueness and Existence, as well as Euler's method for two systems, I tried using them to no avail. I also attempted to calculate dy/dx or manipulating the equations but that didn't work either.

The teacher said that we could start by assuming the opposite and try to find a contradiction, but I don't know how to use that information in any way.
Any help or nudge in the right direction would be greatly appreciated (Happy)