1. ## differential equations

(D@@2)(y)(x) + x^2(y(x))^2=x, y(0)=y(2)=0 (1)
let :=(D@@2)(y)(x)+x^2*(y(x))^2=x, y(0)=0,y'(0)=a (2)
plot the solution to (2) for a = 2.
plot the solutions to (2) for at least four a values of your choice in the range [-0:6; 3]. What does this tell you about the solution to (1) that we found earlier?
so what does this tell me about my solution to (1)?
please could you explain clearly why you can conclude what you can so I fully understand?
many many thanks for your time and effort - much appreciated

2. Do you have to use such opaque notation?

Clearer is d^2y/dx^2+ x^2y^2= x but best is to use LaTex:
$\frac{d^2y/dx^2+ x^2y^2= x$

That is a non-linear differential equation. Since you are asked to draw graphs, at just a few points, I suspect that you are to do a numerical solution. Certainly, we can't tell you what your graph of (2) tells you about (1) if we can't see your graph!

3. apologies for the format

these are my graphs to (1) and (2) respectively.. for (2) my values of a are: -0.6,0,1,3

many thanks