Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Problem with first-order nonlinear ordinary differential equation

  1. Jan 22, 2010 #1
    i have problem to find the solution for : (3x3y+2xy+y3)+(x2+y2)dy/dx=0

    i have tried the exact equation method :

    (3x3y+2xy+y3)dx+(x2+y2)dy=0

    thus M(x,y)=(3x3y+2xy+y3)

    and N(x,y)= (x2+y2)

    then deltaM/deltay=3x3+2x+3y2
    and deltaN/deltax=2x

    Since deltaM/deltay does not equal to deltaN/deltax, this imply that the eqution is not exact

    thus, finding/searching for integrating factor :

    1. 1/N(deltaM/deltay-deltaN/deltax)=(3x3+3y3)/(3x3y+2xy+y3)

    y cannot be eliminated . thus, this is a function of both x and y, not just x

    2. 1/M(deltaN/deltax-deltaM/deltay)=(3x3+3y2)/(x2+y2)

    x cannot be eliminated . thus, this is a function of both x and y, not just y


    thus i cannot find the integrating factor in order to solve the DE. where i'm gone wrong? can somebody point it out? i guess may be in algebra...
     
  2. jcsd
  3. Jan 22, 2010 #2
    You are on right direction. But not all of ODEs have an easy integrating factor.
     
  4. Jan 22, 2010 #3
    is there anyway for me to solve the de? please help me....
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook