For the first question, I am only supposed to find the general solution of the differential equation.(adsbygoogle = window.adsbygoogle || []).push({});

1)dy/dt = -2ty + 4e^(-t^2)

dy/dt + 2ty = 4e^(-t^2)

Integrating factor = e^(Integral of 2t) = e^(t^2)

Multiply both sides by IF:

e^(t^2) * (dy/dt +2ty) = 4e^(t^2-t)

e^(t^2)*dy/dt +2te^(t^2)y = 4e^(t^2-t)

e^(t^2)y' + (e^(t^2))'y = 4e^(t^2-t)

(e^(t^2)y)' = 4e^(t^2-t)

Take integral of both sides:

e^(t^2)y = (integral of) 4e^(t^2-t)

The right hand side is impossible to integrate (unless I'm missing something?). So we just divide both sides by e^(t^2) and leave that as our answer. There was an example in the book where a problem was left like this because the integral was impossible to do, so I'm assuming this is a 'legal' thing to do.

2)Solve the initial value problem of dy/dt = -2ty + 4e^(-t^2)

This is the exact same problem, just with an initial value problem. I dont understand how to do this with an integral on the right hand side. I have a feeling the answer would involve an integral with bounds but im kinda grasping at straws on that one.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Integrating Factors

**Physics Forums | Science Articles, Homework Help, Discussion**