Solve y''=1+(y')2 in two ways, for x is missing and y is missing.
Integration, and reduction of order.
The Attempt at a Solution
First method: (this is correct)
y''=1+(y')2 let y'=p and y''=p'
solve for p: p=tan(x+c)
Substitute back for p=y'
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)
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..