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I'm in the second week of an Elementary Diff. Eq. course and the professor gave us an optional problem that is way beyond the scope of what we've discussed just as a challenge, and I don't know how to approach it. Any advice or related literature would be appreciated. The problem is below.

$$R\, (1+(y')^2)^\frac{1}{2}=xy'',$$ R is a rational constant. Initial conditions: $$y(a)=0, \quad y'(a)=-b/a,$$ $a, b$ are also rational constants.

Any help would be appreciated. All we've done so far is solve linear first-order problems. Thank you.

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up vote 6 down vote accepted

put $y'=z$ and try to reduce order

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And will i put the ${y''=Z'}$ ? –  Ahmed Osama Mar 24 at 12:56

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