(D@@2)(y)(x) + x^2(y(x))^2=x, y(0)=y(2)=0 (1)

This is my task:

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