I will try to explain this with an analogy.(adsbygoogle = window.adsbygoogle || []).push({});

Let's have this equation:

x^2 =9

And let's assume I don't know algebraic methods to solve it, so I create a list using excel with different values. And I see that if I put x=4 it doesn't work, if I put x=5 it is even worse and so on. But If I put 3.9 I see it gets closer to 9, if I put 3.8, 3.7 it gets closer and closer so finally I found x=3 just by trial and error.

My question is, let's have a differential equation:

dy/dx + (dy/dx)^2 = 0

ANd let's say I want to use the previous method to find a dy/dx in a very specific point, let's say the point (0,1). The question is, Can I be sure it will converge?

With an algebraic equation even if I don't know a method to get the general solution using radicals I am able to get solutions just by substituting values and watching if they work or not. Can I do the same with differential equations?

Just by using different straight lines with different slopes and testing if they work on a very specific point, Can I be sure the values will converge to a solution?

Maybe not and I create an immense list of values with excel and I don't see the data geting closer to any slope, i don't know.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Doubt about convergence test on differential equations

**Physics Forums | Science Articles, Homework Help, Discussion**