Have you consdiered substituting the given values for p and t?
Note: Is it "p" or "P". Normally, it's bad form to be switching about.
dP/dt = te^(t+P) ; where P = 1 when t = 0.
I got to the part where:
dP/(e^P) = te^t dt
Found the integral:
-e^(-P) = te^t - e^t + c
Not sure how to find the solution. (we also can't ln a negative).