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n1=10
n2=10
y1=13.59213
y2=10.30381
s1=4.33921
s2=2.24027

F0 = s1^2/s2^2
pf(F0, n1-1, n2-1, lower.tail = F) * 2

[1] 0.06192649

sp = sqrt(((n1-1)*s1^2 + (n2-1)*s2^2)/(n1 + n2 - 2))

t0 = (y1 - y2) / (sp*sqrt(1/n1 + 1/n2))
t0

[1] 2.129375

pt(abs(t0), n1 + n2 - 2, lower.tail = F)*2

[1] 0.04728212