4.2.2 Existence and uniqueness for non-linear second order ode

4.2.2.1 Example
4.2.2.2 Example

Now the ode is written in the form

y=f(x,y,y)y(x0)=y0y(x0)=y0

Then if f is continuous at (x0,y0,y0) and fy is also continuous at (x0,y0,y0) and also fy is also continuous at (x0,y0,y0) then there is unique solution on interval that contains x0.