Question

differential equation in calc 2
dR/dx=a(R^2+1)
I separated the variables, but I end up with
R^3+R=3ax+C
which I'm then not sure how to solve for R

Answer 1

I think you made a mistake with the separation of variables:
\[\frac{ dR }{ dx }=a(R^2+1)\]\[\frac{ dR }{ R^2+1 }=adx\]Now I think that \[(\arctan R)' = \frac{ 1 }{ R^2 + 1 }\]Does this help you enough, or do you want me to go further?