In: Advanced Math
5) Solve 2yy’’ = 1 + (y’)^2
Let
,
then
Moreover,
Substituting the value of in the given question, we get
Intergrating both sides, we get
Thus,
where . Using above equation to find the value of , we get
Integrating both sides we get
Squaring both sides we get
Since we had a second order differential equation, we have got two solutions one corresponding with and another one with .