Expressing erfi using "regular" functions (ODE)

by nahm8 fkn8   Last Updated November 10, 2018 01:20 AM

I've been given a linear first order differential equation which can be written as $ x'(t)+p(t) x(t)= q(t)$. The general solution formula given is: $x(t)={e^{-P(t)}} \int {e^{P(t)}} \cdot q(t) dt + C {e^{-P(t)}}$ where C is our constant. Specifically, I've been given the DE $ x'(t)+2tx(t)=2t^2 $ and I've been asked if it is possible to use the general solution formula (stated above) to find a solution to the DE which only contains "regular/ordinary" functions. I know I get an erfi function, but the point of the question is to ask if it is possible to write the solution in a different way. Is this possible? If it is, how would I go about it?

So far I've tried to figure out if I might be able to use the derivative of the erfi solution to express the solution using regular functions.

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