Question

Sketch the solution to the initial value problem and determine its maximum value.

Answer 1

\[dy/dt=2y-2yt\]

Answer 2

y(0)=3

Answer 3

\[ \frac{dy}{dt} = 2y(1-t)\]
\[ \frac{dy}{y} = 2(1-t)dt\]
Integrating both sides, \( \ln y = 2(t - t^2/2) +C\) , put the value 0,3
you get, c = ln(3)

put the value of C ... and get your answer