diff --git a/youtube_dl/extractor/udemy.py b/youtube_dl/extractor/udemy.py
index e2bab52fe..4a0eaf65f 100644
--- a/youtube_dl/extractor/udemy.py
+++ b/youtube_dl/extractor/udemy.py
@@ -77,7 +77,11 @@ def _login(self):
         login_popup = self._download_webpage(
             self._LOGIN_URL, None, 'Downloading login popup')
 
-        if login_popup == '<div class="run-command close-popup redirect" data-url="https://www.udemy.com/"></div>':
+        def is_logged(webpage):
+            return any(p in webpage for p in ['href="https://www.udemy.com/user/logout/', '>Logout<'])
+
+        # already logged in
+        if is_logged(login_popup):
             return
 
         login_form = self._form_hidden_inputs('login-form', login_popup)
@@ -95,8 +99,7 @@ def _login(self):
         response = self._download_webpage(
             request, None, 'Logging in as %s' % username)
 
-        if all(logout_pattern not in response
-               for logout_pattern in ['href="https://www.udemy.com/user/logout/', '>Logout<']):
+        if not is_logged(response):
             error = self._html_search_regex(
                 r'(?s)<div[^>]+class="form-errors[^"]*">(.+?)</div>',
                 response, 'error message', default=None)