Your sister is drawing a family of circles through the origin with centers on the x-axis using the Desmos online plotting tool. You want to impress her with your knowledge of differential equations...

solve in differential equation

Extracted text: Your sister is drawing a family of circles through the origin with centers on the x-axis using the Desmos online plotting tool. You want to impress her with your knowledge of differential equations and told her that you can draw the corresponding orthogonal trajectories of the family of circles that she is plotting. Find the equation of the orthogonal trajectories.