When comparing and contrasting, it's always good to think about what your doing it with. I'm not going to give to a full paragraph, but I'd love to help get one started for you!
First, let's look at the definition of both terms:
-Design: "<span>purpose, planning, or intention that exists or is thought to exist behind an action, fact, or material object" ~ Google
-Problem Solving: "Taking different approaches to finding a solution to the problem, or task at hand."
Now, let's compare. When designing things, you in a way, are problem solving to figure out how to create or build a solution to a problem. This can be through trial and error, or complex thinking.
Problem solving is related to design in various ways. Deciding what steps or details of how to create artwork is in part problem-solving, and it allows you to create a design or illustration as you do this. This can be considered as Computer Science as well. Every detail, size, direction, shape, strength, contrast, and so forth in design must be put in the right order in the right way, and making the best decision to achieve what you want is "problem solving" and correlates to the design you are mending.
