Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Ordinary Differential Equations
Let F be the family of curves given by
x2 + 2hxy + y2 = 1, − 1 < h < 1 .
Then, the differential equation for the family of orthogonal trajectories to F is
1
(x2y − y3 + y) \(\frac{d y}{d x}\) − (xy2 − x3 + x) = 0
2
(x2y − y3 + y) \(\frac{d y}{d x}\) + (xy2 − x3 + x) = 0
3
(x2y + y3 + y) \(\frac{d y}{d x}\) - (xy2 + x3 + x) = 0
4
(x2y + y3 + y) \(\frac{d y}{d x}\) + (xy2 − x3 + x) = 0