  Spherically symmetric cosmological equations in the usual FLRW coordinates
are explored, with different sources. The first couples a perfect fluid with a
quintessence scalar field and the second couples a perfect fluid to a tachyonic
scalar field. In both cases, in the inflationary regime, the scale factor a(t)
and its first two time derivatives are positive definite. Both sources in the
matter phase yield a scale factor and its first derivative as positive
definite. In both cases and in each phase, the general solutions of the
differential equations together with the algebraic and differential
inequalities are obtained. As special cases, exponential, hyperbolic, and power
law inflation, as well as power law expansion for the matter phase are all
derived from the general solutions. With recent data on baryonic matter, Hubble
parameter and deceleration parameter, the relative percentages of baryonic
matter, daek matter and dark energy are calculated. The quintessence model
yields: 4% baryonic matter, 18% dark matter, and 78% dark energy. The tachyonic
model gives: 4% baryonic matter, 36% dark matter, and 60% dark energy.
