I have a homework problem where I am to find y_2 for a 2nd ODE, with y_1=x.(adsbygoogle = window.adsbygoogle || []).push({});

I'm familiar with the process of:

let y_2 = ux

y_2- = u'x u

y_2'' = 2u' + u''x

substituting these terms into the 2ODE, then letting u' = v.

When integrating v and u' to solve for u, do I need to include integration constants at both steps?

I have a textbook that suggests that integration constants can be made redundant by choosing the 1 and 0 as their values.

However, I have lecture notes which seem to include integration constants in the final solution.

What's the correct approach?

Thanks

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# 2nd ODE, Reduction of Order, Basis known

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