A Level H2 Math - Differential Eqns

• Jasmine ngjiamin

  17 Dec 13, 12:40

  Hi I've been stuck at this question for quite some time...

   

  Q. Find the general solution of the following differential eqn:

  dy/dx = y (1-y)

  Ans: y = Ae^x/(1+Ae^x)

   

  This was my solution: 

  [1/y(1-y)] . dy/dx  =  1

  
  

  [1/y(1-y)] . dy/dx  =  /1 . dx

  
  

  / [1/y(1-y)] . dy = x + c

  
  

  And I got stuck

  please help me thanks :)
• Mad Hat

  17 Dec 13, 17:27

  For this type of integral:

   ∫ 1/y(1−y) dy

  use partial fractions, break up like this:

   ∫ 1/y + 1/(1−y) dy

  Then easy to get:

   ln|y| − ln|1−y|

  After that still got some algebra, but should be ok already ..

• Jasmine ngjiamin

  17 Dec 13, 20:08

  thanks alot :)