Question

Q: . 1 t ce -24 The orthogonal trajectones of the family of curves x²= 2y-17 where C is an arbitrary constant is given by the family of curves.

Answer 1

solution: 24-1+ cezy Geiven = (1) Differentiating with respect to se, we get 2x=2 dy -o-zeezy dy 24 dy dr or dre dy (1- ce ore, D or dy = x cezy From (1) we get (3 In eenzy = 22-2 using (3) from (2) we get dy dua ay-az da We get Replace dy by ay dae a 25-2 ay sehing or, 20-24 dy op, 2-24 or, ar 2 y = a or, dy dy + 2 y = = x CS Scanned with CamScanner

Integrating factor of (4) is el dx = elogx of (1) by integrating factoon We get multiplying both side = X.32 da Integrating we get you = sad da tk CA you + tk which is required family of orthogonal trajectories. CS Scanned with CamScanner