Ok, I'm stuck! I've tried everything and can't seem to solve this problem!
dy/dt+2y=1 y(0)=5/2; and find the value of the function t=3seconds
I first tried: dy=1-2y dt
then dy/1-2y=dt
next integrate both sides: u=1-2y u'=-2 dx=-1/2du=t
so after integrating: -1/2ln(1-2y)=t+C
When I plug in the IVP, I'm getting a negative log, So now I'm stuck!
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There are two approaches that will give you a greater chance of success:
1. Since the boundary condition will cause 1 - 2y to be negative, re-write the DE as , integrate in the usual way and then include the boundary condition in the usal way, or
2. Make y the subject before using the boundary condition.