1. The problem statement, all variables and given/known data Solve the ODE, 4(dy/dx)=4-y^2 2. Relevant equations 3. The attempt at a solution separating the variables, dy/(4-y^2)=dx/4 then integrating both sides (1/4) ln((2-y)/(2+y))=x/4+c Multiply by 4, so now the constant is different, so must i use a different variable for the constant? ie ln((2-y)/(2+y))=x+c' (2-y)/(2+y)=(e^x)(e^c') y=(2-2(e^x)(e^c'))/((e^x)(e^c')+1) then here, 2(e^c') is another constant, do i have to use another variable to represent it? And also what's the definition of arbitrary constant?