> restart;

> G:=(x,y)->piecewise(y>=0 and y<=x, y*(1-x), x<=y and y<=1, x*(1-y));

> x:='x':f:='f':sol:=int(G(x,y)*f(y),y=0..1);

> assume(x>0);additionally(x<1);

> f:=x->x^2;

> u:=eval(sol);

> assume(z>0);additionally(z<1);

> ode :=-diff(diff(v(z),z),z) =z^2;

> dsolve({ode,v(0)=0,v(1)=0},v(z));

>