Finding the General Solution for a Second Order Differential Equation

[Daniel D]

Hi,

I came across the following differential equation:

$$\sqrt{1+(y')^2}=\frac{d}{dx}\left(y\frac{y'}{\sqrt{1+(y')^2}}\right)$$

I found possible solutions: $$y\left(x\right)=cosh(x+C_{1})$$.
However, this is a second order ODE so there exist a more general solution, with 2 freedom degrees.

Can anyone find it?

Thank you.

 

[berkeman]

Hi,

I came across the following differential equation:

$$\sqrt{1+(y')^2}=\frac{d}{dx}\left(y\frac{y'}{\sqrt{1+(y')^2}}\right)$$

I found possible solutions: $$y\left(x\right)=cosh(x+C_{1})$$.
However, this is a second order ODE so there exist a more general solution, with 2 freedom degrees.

Can anyone find it?

Thank you.

What do you mean "can anyone find it"? Please show us how you have tried to find it so far. This is the PF, not Yahoo answers.