Question

Find a one-parameter family of solutions of the differential equation dy/dt = 4y +1

Answer 1

separate variables
\[\frac{dy}{4y+1} = dt\]
integrate both sides
\[\frac{1}{4} \ln (4y+1) = t +C\]
\[4y+1 = e^{4t+C}\]
\[y = \frac{ke^{4t} -1}{4}\]

Answer 2

I guess the whole "one-parameter" condition doesn't make it any different than a regular separation of variables and integrate O.o

Answer 3

yeah i think they are referring to the constant of integration...there is only 1 constant

Answer 4

Yeah, my best guess, too. Makes sense :P I haven't done too much with DEs, but theyre fun :D

Answer 5

Cheers! My biggest problem always seems to be interpreting the questions.