(adsbygoogle = window.adsbygoogle || []).push({}); 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Differential equation

**Physics Forums | Science Articles, Homework Help, Discussion**