Dy:'diff(y,x)$
F:Dy^2-9*y^2+2*y*sin(x)-x^2*exp(x)$
DFy:diff(F, Dy)$
S:diff(DFy,x)+diff(DFy,y)*Dy+diff(DFy,Dy)*'diff(y,x,2)$
Fy:diff(F,y)$
E:Fy-S;
sol:ode2(E=0,y,x);
Dsol:diff(sol, x);
x1: 0$
y1: 1$
x2: 1$
y2: -1$
linEq1: subst([x=x1,y=y1],sol);
linEq2: subst([Dy=diff(rhs(sol),x), y=rhs(sol),x=x2], DFy) = 0;
con: solve([linEq1, linEq2], [%k1,%k2]);

lab3ans: subst([con], sol);
lab2ans: bc2(sol, x=-0, y=1, x=1, y=-1);
plot2d([rhs(lab2ans), rhs(lab3ans)],[x,0,1],[xlabel,"x"],[ylabel,"y(x)"]);