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If $ \ y'=y \ g(x,y) $ and suppose that $ \ g \ \ and \ \ \partial g / \partial x $ are defined and continuous for all x,y . Then show that $ \ y(x)=0 $ is a unique solution . (Use Intermediate value theorem) $$ $$ I can prove the uniqueness of the solution but i can't show how $ y(x)=0$ is a solution. Please someone help me

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  • $\begingroup$ It's pretty obvious $y=0$ is solution. How did you prove the uniqueness? $\endgroup$ – user261263 Apr 2 '17 at 12:12
  • $\begingroup$ i have tried to show that y' >0 or y'< 0 , the y(x) is strictly monotone and hence by intermediate theorem y=0 is unique $\endgroup$ – M. A. SARKAR Apr 2 '17 at 12:17
  • $\begingroup$ Replace $y(x)$ in the RHS of the equation and see what happens with $y'$. $\endgroup$ – Abelois Apr 2 '17 at 12:17
  • $\begingroup$ then what is the use of g and g(x,y) ? $\endgroup$ – M. A. SARKAR Apr 2 '17 at 12:19

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