F:  'diff(y,x)^2 + 2*y^2 + 3*y*exp(2*x)*sin(x) - 5*cos(x);
Dy:  'diff(y,x);
FDy:  diff(F,Dy);
eqn: diff(FDy,x) + diff(FDy,y)*'diff(y,x) + diff(FDy,Dy)*'diff(y,x,2) - diff(F,y) = 0;
eqn2:subst(Dy='diff(y,x),eqn)$
sol:ode2(eqn2,y,x)$
sol2:bc2(sol, x=0, y=1, x=2, y=2)$
f:subst([x=0,y=1],sol);
eq2:subst([Dy=diff(rhs(sol),x),y=rhs(sol)],FDy=0)$
eq2:subst([x=1],eq2)$
con:solve([f,eq2],[%k1,%k2]);
con2:subst(con,sol);
wxplot2d([rhs(sol2),rhs(con2)],[x,0,1],[xlabel,"X"],[ylabel,"Y"]);