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Does there are differential equations of the form $y'=f(x,y),y(x_{0})=y_{0}$ which has exactly two solutions. Actually i have only differential equations which has either no solution or unique solutions or infinitely many solutions. Thanks.

neelkanth
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    There are always infinitely many solutions in the non-uniqueness case. The theorem is due to Kneser. See here: https://math.stackexchange.com/questions/657284/if-an-ivp-does-not-enjoy-uniqueness-then-there-are-infinitely-many-solutions – Alex R. Jul 27 '17 at 17:43
  • Thanku............... – neelkanth Jul 28 '17 at 07:13

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