dy/dt = y + 2
y(0) = 3
find y(2)
It's mainly the combination of dy/dt and y in the equation that's causing my confusion. Does this mean that when I take the antiderivative, I need to substitute so that it is with respect to y?
then
after moving differentials and integrating. Taking the antiderivative,
which, after solving for y, leads to
Plugging in y(0)=3, and after solving for C, C = 5.
So our specific solution is . Feel free to verify this by differentiating and using initial conditions. Finding y(2),
.
(As a side note, go Ovie!)