The function has to be determined for which the differential equation `dy/dx = (1+x)(1+y^2)` holds.
It can be seen that the function should be such that the term (1+x) can be factored from the expression for `dy/dx` .
The rule for differentiation of nested functions has to be used for all the given options. But only for `y = tan(x^2/2 + x + c)` the derivative of `(x^2/2 + x + c)` is equal to x + 1
The correct answer is D, `y = tan(x^2/2+x+c)`