Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I just started playing with higher order ODEs and I'm stuck in one particular step. Here it is:

[tex]

y^{''} + y = \frac{1}{\cos x}

[/tex]

1. step:I find fundamental solution system, which in this case is

[tex]

[\cos x, \sin x]

[/tex]

So general solution looks like this:

[tex]

y(x) = \alpha\cos x + \beta \sin x

[/tex]

Using the method of variation of parameters, [itex]\alpha[/itex] and [itex]\beta[/itex] become functions of x:

[tex]

y(x) = \alpha(x)\cos x + \beta(x) \sin x

[/tex]

[tex]

y'(x) = \alpha^{'}(x)\cos x - \alpha(x)\sin x + \beta^{'}(x) \sin x + \beta(x) \cos x

[/tex]

Now I don't understand the condition

[tex]

\alpha^{'}(x)\cos x + \beta^{'}(x) \sin x = 0

[/tex]

Why does it have to be so?

Thanks for explanation!

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# Homework Help: Why this condition in ODE?

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