Solve Eq: y''(x)+(2/x)y'(x)+(w^2)y(x)=0

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Dear All,

I am having a problem finding the solution for this eq:

y''(x)+(2/x)y'(x)+(w^2)y(x)=0

I know it is quite elementary! any pointers will be much appreciated!

thanks
 
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no body wants to help even with a suggestion! :(
 
Hi !

The change of function y(x) = f(x)/x will transform the ODE into a very simple linear ODE with constant coefficients.
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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