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Ok, I know how to separate variables in solving an ODE. I am unable to understand a solution I have for a problem which was the result of reduction of order- we end up with u''*sinx-2u'*cosx=0

so turn this into u''/u'=-2cosx/sinx

At this point I don't understand the process. I've tried looking at it as making the left side a "u substitution", or rewriting it d(du/dt)/dt / du/dt and integrating both sides,

also, tried making a substition w=u', but this seems hard to get u back in the end.

Can someone explain thoroughly what the process looks like in solving this?

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# Separation of variables , but for 2nd order

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