differential

eq1:x^2*y=1+c*x;
eq2:solve(eq1,y);

eq3:subst(y=y(x),eq2);
eq4:diff(eq3,x);
eq5:subst(y(x)=y,eq4);

eq6:solve(eq5,c);
eq7:subst(eq6,eq1);
eq8:lhs(eq7)-rhs(eq7)=0;
ode2(eq8,y,x);
ratsimp(%*x^2);

Is there a simpler way to get from eq3 to eq5?

Tom Dean