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)

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- May 12th 2010, 02:01 PMsbankicasimple question about autonomous first-order DEs
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) - May 12th 2010, 03:00 PMpickslides
Have you solved it yet? What did you get?

- May 13th 2010, 12:39 AMchisigma
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