- #1
bobey
- 32
- 0
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 equation 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...
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 equation 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...