For the Post Slider, edit:
In that file, wrap
x_get_view( 'ethos', '_post', 'slider' ); with the
is_home WordPress Conditional.
For the Post Carousel, edit:
x_get_view( 'ethos', '_post', 'carousel' ); with the same conditional above.
Please note that the WordPress conditionals are part of WordPress development and custom coding them would be the user's responsibility. Issues that will arise from the use of custom codes even taken from this forum and further enhancements of the code should be fixed by you or a third party developer.
Hope that helps and thank you for understanding.