why cant it be solved?

d2y/dx2 + (x^2)(y^2) = x, y(0) = y(2) = 0

why cant this be solved algebraically? or can it?

and if so, how?

many thanks

That's a rather badly non-linear equation. Typically such equations do NOT have what you call an "algebraic" solution. A better question would be a 'why should it have such a solution?"

ok.. but why should I be able to tell i cant solve it?

why could you tell that it couldnt be solved algebraically?

thanks

I thought that I had just answered that! Only very special (very carefully set up) non-linear equations can be solved "exactly".

sorry to be persistent.. I just want to make sure I understand exactly

so how could you tell straight away that it couldnt be solved? is there a name for such equations? what characteristics make it such that it cant be solved?

many thanks - much appreciated

I believe it is because the second y term is non-linear. A requirement to solve unless it's a special case.