First order differential equation

[elmarsur]

Homework Statement

y is a function of t

Homework Equations

y'+ky(e^-t)=l(e^-3t)

The Attempt at a Solution

Considering that the equation is of the form dy/dt + p(t)y =q(t) , I have been looking for an integrating factor of the form: e^{integral[p(t)dt]}, where p(t) = ke^(-t)
If I calculated correctly, the integrating factor I found is (-t).
Multiplying both sides of the original equation just brought me to a new full stop.

Thank you very much for any guidance and correction.

 

[Dick]

How did you calculate the integral of k*e^(-t) and get (-t)??

 

[elmarsur]

Thank you!
I ended with integrating factor y = e^{-k*e^(-t)}
I took ln of both sides but wrote it wrongly. Nonetheless, if I get ln(y) = k*ln(t) I still don't know how to follow.
Unless, of course, this is not right either.

Thank you for any input.