Dy:'diff(y,x)$
F:(Dy)^2+9*y^2+2*sin(x)*y-(x^2)*%e^(x)$
FDy:diff(F,Dy)$
eqn:diff(F,y)-(diff(FDy,x)+diff(FDy,y)*'diff(y,x)+diff(FDy,Dy)*'diff(y,x,2))=0$
eqn2:subst(Dy='diff(y,x),eqn)$
sol:ode2(eqn2,y,x)$
sol2:bc2(sol, x=0, y=1, x=1, y=-1)$
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);
plot2d([rhs(sol2),rhs(con2)],[x,0,1],[xlabel,"Ось X"],[ylabel,"Ось Y"]);