What is a solution to the differential equation dy/dx=(1+x)(1+y)?

#dy/dx=(1+x)(1+y)#

this is separable!

#1/(1+y) dy/dx=1+x#

so we integrate both sides

#int \ 1/(1+y) dy/dx \ dx=int \ 1+x \ dx#

or

#int \ 1/(1+y) \ dy=int \ 1+x \ dx#

#ln (1+y) = x + x^2 / 2 + C#

#1+y = e^(x + x^2 / 2 + C)#

#y =C e^(x + x^2 / 2 ) - 1#