# A Derivatives of functions in ODE

1. Apr 9, 2016

### LagrangeEuler

For ordinary differential equation
$$y''(x)+V(x)y(x)+const y(x)=0$$
for which $\lim_{x \to \pm \infty}=0$ if we have that in some point $x_0$ the following statement is true
$y(x_0)=y'(x_0)=0$ is then function $y(x)=0$ everywhere?

2. Apr 10, 2016

### Strum

I suppose you mean $\lim_{x=\pm \infty} y(x) = 0$? And no the function doesn't have to be $0$ everywhere. An example is $y(x) = \tanh(x)^{2}(1-\tanh(x)^{2})$. (You will have to work out $V(x)$ yourself.)

3. Apr 10, 2016

### LagrangeEuler

Yes $\lim_{x \to \pm \infty}y(x)=0$. Interesting example. Look here

from 2:46 - 4:09.

4. Apr 10, 2016

### Strum

Well $V(x)$ in the above solution is divergent in $0$. The product of $V(x)y(x)$ still exists.

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