Give the family of orthogonal trajectories of f) None of the above. Solution y = cx^5 - 4 So, c = (y + 4)/x^5 dy/dx = 5Cx^4 Replace c : Now, dy/dx = 5x^4 * (y + 4) / x^5 dy/dx = 5(y + 4) / x Since this is orthogonal, slope must be -x/(5(y+4))..... dy/dx = -x/(5(y + 4)) We can now solve this by separation opf variables... 5(y + 4)dy = -xdx Integrating : 5y^2/2 + 20y = -x^2/2 + C Multiply all over by 2 : 5y^2 + 40y = -x^2 + C C = x^2 + 40y + 5y^2 Option A.