find the orthogonal trajectory of y = (k/x)
first we find the diff. equation of the given family
y=(k/x) -----------(1)
diff. w.r.t. x
y' = -k / (x²)---------(2)
eliminating k , divide (2) by (1)
y' / y = -1/x ---------(3)
(3) is the diff. equation of the given family.
replace y with -1/y' in (3) to get the diff. equation of the orthogonal trajectory
diff. equation of the orthogonal trajectory is
-yy' = -1/x
y(dy/dx) = 1/x
ydy =xdx
integrating and simplifying, we see that the orthogonal trajectory is
x² - y² = C
disclaimer:
There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.
No comments:
Post a Comment
please leave your comments