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:

$\displaystyle dx/dt=x^2 +y$

$\displaystyle dy/dt=x^2 y^2$

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 $\displaystyle x(t)-> infinity$ as $\displaystyle t->t*$. 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