For this case we have the following difference equation:
[tex] dy / dx = 3xy
[/tex]
Applying separable variables we have:
[tex] dy / y = 3xdx
[/tex]
Integrating both sides we have:
[tex] \int\ ({1/y}) \, dy = \int\ {3x} \, dx [/tex]
[tex] ln (y) = (3/2) x ^ 2 + C
[/tex]
applying exponential to both sides:
[tex] exp (ln (y)) = exp ((3/2) x ^ 2 + C)
y = C * exp ((3/2) x ^ 2)[/tex]
For y (1) = 1 we have:
[tex]C = 1 / (exp ((3/2) * 1 ^ 2))
C = 0.2[/tex]
Thus, the particular solution is:
[tex] y = 0.2 * exp ((3/2) x ^ 2)
[/tex]
Whose domain is all real.
Answer:
y = 0.2 * exp ((3/2) x ^ 2)
Domain: all real numbers
