E-field of solid sphere with non-uniform charge density

mncyapntsi
Homework Statement:
Charge is distributed throughout a spherical volume of radius R with a density
where is a constant. Determine the electric field due to the charge at points both inside and outside the sphere.
Relevant Equations:
netEflux = qin/e0, and EA = qin/e0
Hi! I've been trying to attempt this problem over here but the solutions state that the solution is this below?

However, from integrating the density and then plugging it into Gauss's law, I get the exact same thing, except a 15 instead of a 5. Could any please help point out if there is an error on my part, or if there is perhaps a type on the solutions?
Thanks a lot!

Staff Emeritus
Homework Helper
Gold Member
Your post is missing many relevant equations

Staff Emeritus
Edit: Is the given charge density $$\rho=ar^2$$? If yes then the book solution is correct.