- #1
thereddevils
- 438
- 0
Homework Statement
Solve the ODE, 4(dy/dx)=4-y^2
Homework Equations
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?