LInear 1st order differential

R(x)= exp (integrate p(x) dx)

integrate p(x)dx = integrate -tanx dx = integrate -sinx/cosx dx = integrate 1/cosx d(cosx) = ln(cosx)

R(x) = exp [ln(cos(x))] = cosx

y=1/R(x) integrate R(x)q(x) dx

integrate R(x)q(x) dx = integrate cos(x) sin^2(x) dx = integrate sin^2(x) d(sin(x)) = 1/3 sin^3(x) + c

so y = sec(x)(1/3 sin^3(x) + c)
y(0) = c = 1
finally y = sec(x) (1/3 sin^3(x) +1)