Easy Seperable Differential Equation Domain Questions

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SUMMARY

The discussion centers on a separable differential equation problem from the Boyce and DiPrima Elementary Differential Equations textbook. The user, Dane, initially believes the solution is defined on the intervals (-inf, -2) ∪ (-2, 3) ∪ (3, inf), but is corrected by another participant who confirms that the solution is valid only on the interval (-2, 3). The boundary conditions specified in the problem restrict the solution's validity, making the book's assertion accurate.

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  • Understanding of separable differential equations
  • Familiarity with boundary conditions in differential equations
  • Knowledge of interval notation and its implications
  • Experience with the Boyce and DiPrima Elementary Differential Equations textbook
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danerape
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This is a problem from the Boyce and Diprima Elementary DE book. I solved this equation
and got the correct solution. However, the author notes that the solution is defined on the
interval (-2,3) only. I have found it to be defined (-inf,-2)u(-2,3)u(3,inf), or EVERYWHERE BUT x=-2, x=3. Is this a mistake in the book or am I missing something?


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Thanks a lot,

Dane
 

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Yes, the book is correct. There exist solutions for x< -2 and x> 3 but they cannot be "connected" to the solution between -2 and 3. The solution satisfying the given boundary condition is valid only between -2 and 3.
 

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