Exact ODEs

Wednesday, 12 September 2018

1:40 PM

Many first order ODEs can be written in the form of

 

We can rearrange this equation to get the form

 

We say that the equation  is exact if

 

 

 

Steps

• Turn into the form
• Differentiate  wrt
• Differentiate  wrt
• Confirm that the differentials are equal to each other
• If not equal, then they are not exact. STOP
• Define  s.t.
• Define  s.t.
• Integrate
• Differentiate  wrt
• Equate with
• Equate
• Integrate
• Sub into