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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)]

Thank you for reading!

Re: Differential equations problem

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