solve : (x^2+y)dy/dx+2xy=0 → (2xy) dx+(x^2+y) dy=0

(X^2+y) dy/dx+2xy=0 → (2xy) dx +(x^2+y) dy=0
in Calculus Answers by Level 12 User (101k points)

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

20 Answers

P_= 2xy ,
by Level 12 User (101k points)
æp/æy= 2x
by Level 12 User (101k points)
& Q_=x^2+y ,
by Level 12 User (101k points)
æQ/æx=2x :
by Level 12 User (101k points)
P,y-Q,x=0
by Level 12 User (101k points)
ln(I•F)=0
by Level 12 User (101k points)
I•F=1
by Level 12 User (101k points)
Therefore the given is an exact equation so that,
by Level 12 User (101k points)
du_= Pdx+Qdy=0
by Level 12 User (101k points)
→ u(x,y)=c,1
by Level 12 User (101k points)
æu/æy = Q
by Level 12 User (101k points)
u=x^2y+y^2/2+w(x) ,
by Level 12 User (101k points)
æu/æx=2xy+w'(x)_=2xy
by Level 12 User (101k points)
→ w'(x)=0
by Level 12 User (101k points)
And w(x)= c2
by Level 12 User (101k points)
Therefore, y^2/2+x^2y+(c2-c1)=0
by Level 12 User (101k points)
→ y^2+2x^2y+c=0
by Level 12 User (101k points)
This is a quadratic in Y with discriminant
by Level 12 User (101k points)
D=(2x^2)^2-4c :
by Level 12 User (101k points)
Y=-x^2 ± ab•sq•rt(x^4 -c)
by Level 12 User (101k points)

Related questions

15 answers
solve: x dy/dx=2xe^x-y+6x^2 → (y-6x^2-2xe^x) dx+ xdy=0
asked Jan 28, 2014 in Calculus Answers by Jennifer A. Cascaño Level 12 User (101k points) | 3.8k views
25 answers
solve: y'-y•COTX=2X-X^2•COTX → (X^2 COTX-Y•COTX-2X) dx+dy=0
asked Jan 27, 2014 in Calculus Answers by Jennifer A. Cascaño Level 12 User (101k points) | 4.2k views
20 answers
solve: (2xy-x^-2 y^-2) dx +(x^2-2x^-1 y^-3) dy=0
asked Jan 30, 2014 in Calculus Answers by Jennifer A. Cascaño Level 12 User (101k points) | 2.5k views
3 answers
solve: (2x^2+2xy+2xz^2+1)dx+dy+2zdz=0
asked Jan 18, 2014 in Algebra 2 Answers by Jennifer A. Cascaño Level 12 User (101k points) | 2.8k views
1 answer
(2x^2y-2y^2+2xy)dx + (x^2-2y)dy=0
asked Aug 12, 2014 in Other Math Topics by Kiroro | 4.0k views
3 answers
(2x²+2xy+2xz²+1)dx+dy+2zdz=0
asked Sep 7, 2012 in Algebra 1 Answers by anonymous | 2.1k views
1 answer
solve: x^2 dx+y•(x-1) dy=0
asked Feb 14, 2014 in Calculus Answers by Jennifer A. Cascaño Level 12 User (101k points) | 1.3k views
40 answers
solve: y^3 dx+2(x^3-xy^2) dy=0
asked Jan 30, 2014 in Calculus Answers by Jennifer A. Cascaño Level 12 User (101k points) | 4.9k views
1 answer
(2x^2 y - 2xy^2 + y)dx + (x - 2y)dy
asked Oct 22, 2019 in Other Math Topics by anonymous | 1.2k views
1 answer
show that (1-x^2)dy/dx+y=0
asked Jun 22, 2017 in Calculus Answers by Poulami | 702 views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!

Most popular questions within the last 3000 days

  1. 50+50-25X0+2+2= (19)
  2. it takes 10 road workers 5 days to complete a road repair when working 2 hours a day.Working at the same pace,how many days will it take 2 people working 5 hours a day to finish it? (3)
  3. Solve 15 -1(12÷4+1)? (4)
  4. 8:4(5+2) (3)
  5. How can i represent 1/3; 3/3; 7/3; 10/3 and 15/3 on a number line? (1)

Most popular tags

87,516 questions
100,279 answers
2,420 comments
732,438 users