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Lelechka [254]
3 years ago
14

Find the domain for the particular solution to the differential equation dy dx equals the quotient of 3 times y and x , with ini

tial condition y(1) = 1.
Mathematics
1 answer:
Svetach [21]3 years ago
6 0
For this case we have the following difference equation:
 dy / dx = 3xy

 Applying separable variables we have:
 dy / y = 3xdx

 Integrating both sides we have:
 \int\ ({1/y}) \, dy =  \int\ {3x} \, dx
 ln (y) = (3/2) x ^ 2 + C

 applying exponential to both sides:
 exp (ln (y)) = exp ((3/2) x ^ 2 + C)

 y = C * exp ((3/2) x ^ 2)
 For y (1) = 1 we have:
 C = 1 / (exp ((3/2) * 1 ^ 2))

C = 0.2
 Thus, the particular solution is:
 y = 0.2 * exp ((3/2) x ^ 2)

 Whose domain is all real.
 Answer:
 y = 0.2 * exp ((3/2) x ^ 2)
 Domain: all real numbers
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