# Math Help - ode uniqueness #2

1. ## ode uniqueness #2

Show that if g and g' are cont. on R and f is cont. on R, then the solution y(t,o,A,B) of

y''+ f(y) y'+ g(y)=0 , y(o)=A, y'(o)=B

exists locally, is unique and can be continued so long as y and y' remain bounded.

Hint: (Use a transformation)

2. Originally Posted by Fibonacci88
Show that if g and g' are cont. on R and f is cont. on R, then the solution y(t,o,A,B) of

y''+ f(y) y'+ g(y)=0 , y(o)=A, y'(o)=B

exists locally, is unique and can be continued so long as y and y' remain bounded.

Hint: (Use a transformation)

A direct application of the known theorem concerning the dependence of autonomous de's on initial data.