Solve newprob so that output actually depends on input

[moble]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

Going through the new example, I saw that the gradient returned (nothing,); checked with ForwardDiff and got all zeros; then just looked at the function value with different inputs, to see that it was indeed identical. It's hard to see this kind of mistake, but the newprob was never actually used; it just re-solved the original problem every time. With this change, I obtain consistent gradients with Zygote, ForwardDiff, and even FiniteDiff.

[ChrisRackauckas]

Thanks!