Solve the differential equation dy/dx=(y^(1/2))*sin(x/2) to find y in terms of x.

Here, we must first rearrange our equation so all x terms are on one side and all y terms are on the other. Multiplying both sides by dx and diving both by y^(1/2) gives us y^(-1/2)dy = sin(x/2)dx, which is a directly integrable equation. Integrating both sides, we get 2y^(1/2) = -2cos(x/2) + c, where c is some arbitrary constant of integration. Rearranging to find y, we get y=(-2cos(x/2) + A)^2, where A=c/2.