Q1
i) Find the othrogonal trajections for the following family of curves.
ii) Sketch on the same set of axes at least three members of each of the two families.
y= A x3
Solution
y= A x3
dy/dx = A 3x^2
now put dy/dx = -dx/dy
since othgonal trajecotries are nothign but which are orthogonal
becuase dy/dx * -dx/dy = -1
multiplication slopes of orthogonal trajectories is -1
-dx/dy = A 3x^2
-dx/dy = 3x^2 y/x^3
-dx/dy = 3y/x
3y dy + x dx = 0
take integration
3y^2/2 + x^2/2 = C
x^2 + 3y^2 = C C is constatn