The Murder Mystery Method to Solve Exact Differential Equations

More documents

Recommendations

Info

Example 1: Check consistency Solve: (3y 2 +4x 3 )dx+(6xy+2y)dy=0Witness M: Witness N:∫2 32 4( 3y + 4x) dx = 3xy+ x( xy + 2y)∫26 dy = 3xy+ yThe clue that contains the two variables (3xy 2 ) was seen by the twowitnesses: Therefore we do trust them and we have our murderer (thefunction whose differential is the left side of the equation):F +2 4 2( x,y)= 3xy+ x y2
Example 1: Final Solution Solve: (3y 2 +4x 3 )dx+(6xy+2y)dy=0Witness M: Witness N:∫2 32 4( 3y + 4x) dx = 3xy+ x( xy + 2y)∫26 dy = 3xy+ yThe clue that contains the two variables (3xy 2 ) was seen by the twowitnesses: Therefore we do trust them and we have our murderer (thefunction whose differential is the left side of the equation):F +2 4 2( x,y)= 3xy+ x yThe implicit solution of the differential equation is22 4 23xy+ x + y =C
Page 5 and 6: Creating a Differential Equation fr
Page 7 and 8: Creating a Differential Equation fr
Page 9 and 10: The mystery we have to solveTherefo
Page 11 and 12: The murderer F and the witnessesM a
Page 13 and 14: If clues are consistent, then you k
Page 15 and 16: Murder Mystery Method Applied to Id
Page 17: Example 1: Interrogation(Integratio
Page 21 and 22: Example 2: Interrogate (Integrate)
Page 23 and 24: Example 2: Final Solution Solve: (y

The Murder Mystery Method to Solve Exact Differential Equations

Create successful ePaper yourself

Delete template?

Save as template?