Just do what the book says, differentiate twice wrt . Use the result of the first differentiation to remove the from the second derivative equation. is a constant so goes out when you differentiate.
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)]
Thank you for reading!