In A Raisin in the Sun, what is the pathlogical and resilient approach to examine the Younger family?

You might want to have another look at this question as it is not particularly clear what it is that you are precisely asking for. I have edited it to make it in to a question rather than a statement, but still you would do well to revise it and consider what specificially you are looking for and what you want to know. Are you, for example, wanting to look at resilience as a theme in this play? This could be considered to be a theme that is worthy of investigation.

The Younger family are incredibly resilient in the way that they stand up to the various pressures that are threatening to pull them apart, both internal and external. As the play begins and develops we identify so many different challenges that are present, from Bennie's desire to study medicine and Ruth's pregnancy. These are confounded as the play develops by pressure placed against them from both the black and white community about their imminent move. Yet in spite of complete financial disaster thanks to the imprudence of Walter and his loss of all money, the family manages to pull together and, in spite of a very uncertain and potentially dangerous future, retain their loyalty to each other and to their dreams against difficult odds.

You might want to think about the symbol of Mama's plant in the play and how it represents the care and responsibility she feels towards her family and her desire to nurture it. This plant, just like the Younger family as a whole, shows itself to be resilient and hardy - Mama expresses pride in its ability to flourish under her care even though it doesn't get enough light and water. There is of course a parallel between Mama's care of her plant and her care of her family, for the family somehow manages to flourish in spite of the less than perfect circumstances they are placed in.

The play ends with a note of optimism as Mama takes the plant, planning to plant it in her new garden and give it more space, just as her family are to be "planted" in a more spacious and better location. Mama's words at the end of the play about her family, "Yeah - they something alright, my children" expresses her belief and faith that they will continue to flourish in spite of the challenges that still face them.