consider the autonomous first-order equation . and the initial condition . How do you go about drawing the graph of a typical solution when
a)
b)
The DE is of 'separable variables type' and can be written as...
(1)
Because is...
(2)
... is also...
(3)
... so that the solution of (1) is...
(4)
... that can be 'explicitate' as function of x as...
(5)
If now we intend to impose the initial condition we 'discover' that we can do it only if is . To overcome the handycap in case we write (2) as...
(6)
... and repeat the procedure obtaining...
(7)
Kind regards