# test0 solution for differential equation with x=0, return 0 is true;


test0(sol_, eq_):= test0(sol,eq,y);
test0(sol_ and sol2_, eq_):= test0(sol,eq,y) and test0(sol2,eq,y);
test0(sol_, eql_=eqr_):= test0(sol,eql-eqr,y);
test0(sol_=sol2_, eq_):= test0(solve(replace(sol-sol2,C_1,1),y),eq,y);
test0(sol_=sol2_, eql_=eqr_):= test0(solve(replace(sol-sol2,C_1,1),y),eql-eqr,y);
test0(sol_=x, y(n_,x_)=eqr_):= n(expand(d(sol,y,n)-replace(1/eqr,x,sol)));
test0(sol_=x, y(n_,x_)+eqr_):= n(expand(d(sol,y,n)+replace(1/eqr,x,sol)));

test0(sol_, eq_,y_):= n(simplify(expand(simplify(replace(tods(eq),y,replace(sol,C_1,1))))));
test0(sol_, eql_=eqr_,y_):= test0(sol,eql-eqr,y);

test0(xx_=a_,yy_=b_, eq1_=eq1r_,eq2_=eq2r_):= (n(replace(simplify(expand(simplify(replace(replace(tods(eq1-eq1r),xx,a),yy,b))))x,0)), n(replace(simplify(expand(simplify(replace(replace(tods(eq2-eq2r),xx,a),yy,b)))),x,0)));