1. The problem statement, all variables and given/known data Solve y''=1+(y')2 in two ways, for x is missing and y is missing. 2. Relevant equations Integration, and reduction of order. 3. The attempt at a solution First method: (this is correct) y''=1+(y')2 let y'=p and y''=p' p'=1+p2 p'/(1+p2)=1 ∫p'/(1+p2)dx=∫1dx arctan(p)=x+c solve for p: p=tan(x+c) Substitute back for p=y' y'=tan(x+c) y=-ln(cos(x+c))+d Second method: (I can't get it to come out as same answer from first method) y''=1+(y')2 let y'=p and y''=p*(dp/dy) p*(dp/dy)=1+p2 From here I can already tell i'm not going to get y=-ln(cos(x+c))+d but this is the method I am told to use..