(D^2y/dx^2 + x^2(y)^2=x, y(0)=y(2)=0 (1)
This is my task:
let :=(D^2y/dx^2)+x^2*(y)^2=x, y(0)=0,y'(0)=b (2)

plot the solutions to (2) for some b values of your choice. What does this tell you about the solution to (1)
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

I have plotted solution, and can see that for b close to -0.6, the graphs are very similar:

I am trying to find the stationary ponts of f(x,y) 5*x^3-12*x-3*x*y+6*y^2-4;

so far, I have got

A:=diff(f,x)=0

B:=diff(f,y)=0

e1:=RootOf(A,x)

e2:=RootOg(B,x)

G:=solve([A,B],[x,y])

do I now need to use allvalues?

if so, I get

V:=allvalues(G). This gives me two values of x and y.  (one with a positive root and one with a negative root)

ie. v=[[x=c - sqrtb,y=4c - 4sqrtb],[x=c+sqrtb,y=4c+4sqrtb]]

r:=diff(f,x$2) =30x

s:=diff(f,x,y) = -3

I am trying to find the stationary ponts of f(x,y) 5*x^3-12*x-3*x*y+6*y^2-4;

so far, I have got

A:=diff(f,x)=0

B:=diff(f,y)=0

e1:=RootOf(A,x)

e2:=RootOg(B,x)

G:=solve([A,B],[x,y])

do I now need to use allvalues?

if so, I get

V:=allvalues(G). This gives me two values of x and y.  (one with a positive root and one with a negative root)

ie. v=[[x=c - sqrtb,y=4c - 4sqrtb],[x=c+sqrtb,y=4c+4sqrtb]]

r:=diff(f,x$2) =30x

s:=diff(f,x,y) = -3