y ' =ò   _____________
Ö1+(y ' )2
 

By Yatir Halevi on Monday, February 18, 2002 - 06:09 pm:

Please help me solve these (describe your steps):
1)

y ' =ò   _____________
Ö1+(y ' )2
 


2)

òy=ò   _____________
Ö1+(y ' )2
 


Thanks,
Yatir

P.s.
I already found out that:

y=ò   _____________
Ö1+(y ' )2
 

Is not solvable

By Andre Rzym on Tuesday, February 19, 2002 - 09:19 am:

If I read (2) correctly, we can differentiate and square to get:

y2 =1+(y')2

This would appear to have the solution y=cosh(x).

Andre

By David Loeffler on Tuesday, February 19, 2002 - 01:31 pm:
And for the first, we get
y ' ' =   ____________
Ö1+y ' 2
 

, so if v=y ' ,
dv/dx=   ____
Ö1+v2
 

. So òdv/(1+v2)1/2=òdx or sinh-1 v=x+c, so v=sinh(x+c), y=cosh(x+c)+d for arbitrary c, d.