1. ## Differential equations problem

Hi there,

I'm studying this topic and am unable to move forward as I can't get to the solution involving r^2! Would someone be so kind as to show me how on earth you get you the second order differential equation in the second picture [equation (5)]

Just do what the book says, differentiate twice wrt $x$. Use the result of the first differentiation to remove the $(y-c)$ from the second derivative equation. $r$ is a constant so goes out when you differentiate.