- #1

- 21

- 0

## Homework Statement

dy/dx=5y(1-y)

y(0)=0.1

x belongs to [0; 2]

## Homework Equations

## The Attempt at a Solution

dy/5y(1-y)=dx

using partial fractions (1/(-y^2+y))=1/(y(1-y))= A/y+B/1-y

multiplying both sides by (y(1-y)) gives 1=A(1-y)+B(y)

when y=0 1=A so A=1

when y=1 1=B so B=1

so 1/(1-y) +1/y =1/(y(1-y))

1/5*(int 1/(1-y)+int 1/(y))=1/5*(-ln (1-y)+ln (y))

so x=1/5*(-ln (1-y)+ln (y))

5x=-ln (1-y)+ln (y)

e^5x=y/1-y

but that doesnt work when y(0)=0.1 does y(0)=0.1 mean when y=0 or when x=0? either way i dont get the right answer plz can someone explain where im going wrong

cheers

dooogle