Series[(1+Sin[x]/x)^(1/4),{x,0,4}]

DSolve[y'[x]==y[x]^2*Cos[x]-y[x]*Cos[x],y[x],x]

DSolve[{y'[x]==y[x]^2*Cos[x]-y[x]*Cos[x],y[0]==2},y[x],x]

Series[(1+x)^{1/4},{x,0,2}]

Series[1/(1+Sin[x]/x),{x,0,4}]

DSolve[y'[x]==2*y[x]^2*Tan[x]-y[x]*Tan[x],y[x],x]

DSolve[{y'[x]==y[x]^2*Cos[x]-y[x]*Cos[x],y[0]==2},y[x],x]

DSolve[{y'[x]==2*y[x]^2*Tan[x]-y[x]*Tan[x],y[0]==2},y[x],x]

Series[1/(1+Cos[x]),{x,0,4}]

DSolve[y'[x]==2*y[x]^2*Cot[x]-y[x]*Cot[x],y[x],x]