Hi, 

   In below code class CaseTriggerUtils
 

trigger CaseTrigger on Case (Before Insert, Before Update,After Insert, After Update){


   if(Trigger.isBefore) {
      CaseTriggerUtils.CaseUtils(Trigger.new);     
   } 
      

}

There is a error in line  
Map<Id, case> c = new Map<Id, case>([select id, casenumber,subject,createddate,ownerid,owner.name from case where subject like :('%' + CaseSubject + '%') order by createddate asc limit 10]);

When i try to update the case i am getting below error. 

Error: Invalid Data. 
Review all error messages below to correct your data.
Apex trigger CaseTrigger caused an unexpected exception, contact your administrator: CaseTrigger: execution of BeforeUpdate caused by: System.QueryException: Non-selective query against large object type (more than 200000 rows). Consider an indexed filter or contact salesforce.com about custom indexing. Even if a field is indexed a filter might still not be selective when: 1. The filter value includes null (for instance binding with a list that contains null) 2. Data skew exists whereby the number of matching rows is very large (for instance, filtering for a particular foreign key value that occurs many times): Class.CaseTriggerUtils.CaseUtils: line 31, column 1

public class CaseTriggerUtils {

 public static void CaseUtils(List<Case> newLst) {  
  
  String FWSubject;
  String RWSubject;
  String CaseSubject;
  
    for (Case c : newLst) {
       system.debug('Case Number :' + c.casenumber); 
       system.debug('Case Subject : ' + c.subject);
       system.debug('Case Subject length : ' + c.subject.length());
       system.debug('Case Owner Name : ' + c.owner.name);
       
       CaseSubject = c.subject;
       
       //Search for FW and RW key word were length of the subject is more than 18
        if(c.subject != null && c.subject.length() > 18){
            if(!c.subject.Contains('FW:')){
              FWSubject = c.subject.replaceAll('FW:','');
              System.debug('FQ Trim String :' + FWSubject);     
         }  
    
        if(!c.subject.Contains('RW:')){ 
         RWSubject = c.subject.replaceAll('RW:','');
         System.debug('RW Trim String :' + RWSubject);   
         }     
       }  
     }
     
   Map<Id, case> c = new Map<Id, case>([select id, casenumber,subject,createddate,ownerid,owner.name from case where subject like :('%' + CaseSubject + '%') order by createddate asc limit 10]);
   
     
   //Search for same case based on subject within 10days. 
   /* list<case> ctendays = [select id, casenumber,subject,createddate,ownerid,owner.name from case where subject like :('%' + CaseSubject + '%') order by createddate asc limit 10];

   for(case ctndays : ctendays){
      system.debug('Existing Cases :'  + ctndays.casenumber + ' ' + ctndays.subject + ' ' + ctndays.createddate + ' ' + ctndays.owner.name);      
   }  */
  
  }

}