Solve Differential Equation with Notation: Reduction of Order Help

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The discussion focuses on solving a differential equation using the Reduction of Order method. The user expresses confusion regarding the notation on the right-hand side, specifically the derivative of y squared over x multiplied by -1. Another participant clarifies that substituting y' with u is an effective first step, leading to the conclusion that y'' can be represented as u'. This exchange highlights the importance of understanding notation and substitution in differential equations.

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I need to solve the following differential equation, And am pretty sure it will require the use of Reduction of Order but have NO clue how do deal with the notation on the RH side, any help Would Be Greatly appreciated.
 

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What's the question about the notation on the RH side? It looks clear enough to me. It's the derivative of y squared over x times (-1). And it does look like substituting y'=u is a good reduction of order first step. So y''=u'. Please continue.
 
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