Assume the next differential LINEAR second order equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]w''+\frac{4}{x}w'+\frac{4}{x^4}w=0[/tex]

So I thought: OK, I need two independent solutions [tex]w_1[/tex] and [tex]w_2[/tex], because the space of solutions is of dimension two.

Then the professor gave us a solution:

[tex]w=sen(2/x)-(2/x)cos(2/x)[/tex]

and I thought: Ok, the solution he's giving us is composed by two linearly independent functions (because doing the wronskian it does not becames zero anywhere),and therefore each function must be solution of the differential equation..

Is this last bolded statement true for any second linear ODE??.

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# Homework Help: Second order ODE question.

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