# Intermediate value theorem 2

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

• It's pretty obvious $y=0$ is solution. How did you prove the uniqueness? – user261263 Apr 2 '17 at 12:12
• 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 – M. A. SARKAR Apr 2 '17 at 12:17
• Replace $y(x)$ in the RHS of the equation and see what happens with $y'$. – Abelois Apr 2 '17 at 12:17
• then what is the use of g and g(x,y) ? – M. A. SARKAR Apr 2 '17 at 12:19