Uniqueness of solutions If differentiable functions y =

Chapter 4, Problem 128E

(choose chapter or problem)

Uniqueness of solutions If differentiable functions \(y=F(x) \text { and } y=G(x)\) both solve the initial value problem

\(\frac{d y}{d x}=f(x), y\left(x_{0}\right)=y_{0}\)


on an interval \(I\) , must \(F(x)=G(x)\) for every \(x\) in \(I\) ? Give reasons for your answer.

Equation Transcription:

Text Transcription:

y=F(x)

y=G(x)

dy/dx = f(x), y(x_0) = y_0

I

F(x)=G(x)

x

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