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I am stuck on the following question:

Assuming $$\frac{d^2y}{dx^2}-q(x)y = 0,\;\; 0 \le x \lt \infty ,\;\;y(0)=1,\;\;y'(0)=1$$ wherein $q(x)$ is monotonically increasing continuous function,then which one of the following is true.

(a) $y(x) \to \infty$ as $x \to \infty$

(b) $\frac{dy}{dx}\to \infty$ as $x \to \infty$

(c) $y(x)$ has finitely many zeros in $[0,\infty)$

(d) $y(x)$ has infinitely many zeros in $[0,\infty)$

I am completely stuck on it.can anyone help me please.

  • 0
    For future reference, you should title your question with something descriptive, preferably with some English, and leave the equations to the actual body of the question.2012-12-17
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    @Babak Sorouh: For better results when searching, I would in general not use any abbreviations.2012-12-17

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