Try the following: Two ways: 1) Using putExtra()  --------  2) Using SharedPreferences
1)
Demo4.class:-----------
public class Demo4 extends AppCompatActivity {
private Button b;
private final String CALL_DEFAULT_MAP = "call_default_map";
@Override
protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.activity_daily__schedule);
    if(getIntent() != null) {//1
        if(getIntent().getStringExtra(CALL_DEFAULT_MAP) != null) {
            if (getIntent().getStringExtra(CALL_DEFAULT_MAP).equals("true")) {
                defaultMap();
            }
        }
    }
    b = (Button) findViewById(R.id.b);
    b.setOnClickListener(new View.OnClickListener() {
        @Override
        public void onClick(View v) {
            Intent myIntent = new Intent(Demo4.this, Demo5.class);
            finish();
            startActivity(myIntent);
        }
    });
}
public void defaultMap() {
            Toast.makeText(getApplicationContext(),"defaultMap()---called",Toast.LENGTH_LONG).show();
}
}
Demo5.class------
public class Demo5 extends AppCompatActivity {
private Button home;
private final String CALL_DEFAULT_MAP = "call_default_map";
@Override
protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.activity_in_route_display);
    home = (Button) findViewById(R.id.home);
    home.setOnClickListener(new View.OnClickListener() {
        @Override
        public void onClick(View v) {
            Intent myIntent = new Intent(Demo5.this, Demo4.class);
            myIntent.putExtra(CALL_DEFAULT_MAP,"true");//1
            finish();
            startActivity(myIntent);
        }
    });
}
} 
2)
Demo4.class---------
public class Demo4 extends AppCompatActivity {
private Button b;
private final String CALL_DEFAULT_MAP = "call_default_map";
private SharedPreferences p;
@Override
protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.activity_daily__schedule);
    p = getApplicationContext().getSharedPreferences("p_key",
            0);//2
    if(p != null){//2
        if(p.getBoolean(CALL_DEFAULT_MAP , false)){
            defaultMap();
        }
    }
    b = (Button) findViewById(R.id.b);
    b.setOnClickListener(new View.OnClickListener() {
        @Override
        public void onClick(View v) {
            Intent myIntent = new Intent(Demo4.this, Demo5.class);
            finish();
            startActivity(myIntent);
        }
    });
}
public void defaultMap() {
    setBoolean(CALL_DEFAULT_MAP , false);//2
    Toast.makeText(getApplicationContext(),"defaultMap()---called",Toast.LENGTH_LONG).show();
}
public void setBoolean(String Name, boolean value)
{
    if(p != null){
        SharedPreferences.Editor editor = p.edit();
        editor.putBoolean(Name, value);
        editor.apply();
    }
}
} 
Demo5.class:----------------
public class Demo5 extends AppCompatActivity {
private Button home;
private final String CALL_DEFAULT_MAP = "call_default_map";
private SharedPreferences p;
@Override
protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.activity_in_route_display);
    p = getApplicationContext().getSharedPreferences("p_key",
            0);
    home = (Button) findViewById(R.id.home);
    home.setOnClickListener(new View.OnClickListener() {
        @Override
        public void onClick(View v) {
            setBoolean(CALL_DEFAULT_MAP , true);//2
            Intent myIntent = new Intent(Demo5.this, Demo4.class);
                            finish();
            startActivity(myIntent);
        }
    });
}
public void setBoolean(String Name, boolean value)
{
    if(p != null){
    SharedPreferences.Editor editor = p.edit();
    editor.putBoolean(Name, value);
    editor.apply();
    }
}
}