kill(all);
F:'diff(y,x)^2-4*y^(2)+2*y+x*exp(2*x);
Dy:'diff(y,x);
Fy1:diff(F, Dy);
ddxFy1:diff(Fy1,x)+diff(Fy1,y)*Dy+diff(Fy1,Dy)*'diff(y,x,2);
Fy:diff(F,y);
Fy-ddxFy1=0;
sol:ode2(Fy-ddxFy1=0,y,x);
sol2:bc2(sol, x=-2, y=0, x=0, y=1);
/*plot2d(rhs(sol2),[x,-2,0],[xlabel,"x"],[ylabel,"y(x)"]);*/
x1: -2$
y1: 0$
x2: 0$
linEq1: subst([x=x1,y=y1],sol);
linEq2: subst([Dy=diff(rhs(sol),x),y=rhs(sol)],Fy1);
linEq3: subst([x=x2],linEq2)=0;

con: solve([linEq1, linEq3],[%k1,%k2]);
sol3: subst([con],sol);
plot2d([rhs(sol2), rhs(sol3)],[x,-2,0],[xlabel,"x"],[ylabel,"y(x)"]);