1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
RideAnS [48]
3 years ago
15

Find Integrating Fector: ylogy dx + ( x-logy )dy=0

Mathematics
1 answer:
12345 [234]3 years ago
4 0
Rewrite the ODE as

y\log y\,\mathrm dx+(x-\log y)\,\mathrm dy=0\iff y\log y\dfrac{\mathrm dx}{\mathrm dy}+x=\log y
\dfrac{\mathrm dx}{\mathrm dy}=\dfrac1{y\log y}x=\dfrac1y

so that it is now linear in x. An integrating factor would

\mu(y)=\exp\left(\displaystyle\int\frac{\mathrm dy}{y\log y}\right)=e^{\log(\log y)}=\log y

Multiply both sides by \mu(y) to get

\log y\dfrac{\mathrm dx}{\mathrm dy}=\dfrac1yx=\dfrac{\log y}y
\dfrac{\mathrm d}{\mathrm dy}[x\log y]=\dfrac{\log y}y
x\log y=\displaystyle\int\frac{\log y}y\,\mathrm dy
x\log y=\dfrac12\log^2y+C
x=\dfrac12\log y+\dfrac C{\log y}
You might be interested in
Use the expression - 8( - 2.5-7).
Paladinen [302]

Answer:

20+56 or basically 76

Step-by-step explanation:

Just multiply -8 to -2.5 and -7.

6 0
3 years ago
Which logarithmic equation is equivalent to the exponential equation 5c=250
Elis [28]

Answer:

c = log_{5}250

Step-by-step explanation:

8 0
3 years ago
Eric bought 21 pounds of sugar for $12 . how many dollars did he pay per pound of sugar?
Stels [109]
$1.75 per pound of sugar
8 0
3 years ago
Can I get your number so we can talk?
solniwko [45]

Answer:

no but you can have my gm/ail

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
4p+25=6(p-3)-3(4-3p)
Wewaii [24]
P = 5 .............................................
this is how= 

first you expand the second equation 
<span>25 + 4p = -18 + -12 + 6p + 9p
</span>
then you add the like terms in the second equation:
25 + 4p = -30 + 15p
then this is how=
25+30 = 15p -4p
55=11p

p= 5

3 0
3 years ago
Other questions:
  • How much trail mix will each person get if 6 people share 3/4 pound trail mix equally
    12·1 answer
  • What else would it be? Parallelogram,rhombus, Trapezoid,rectangle,or square
    13·2 answers
  • Solve for x. −1.5x = −2.55 A) −1.5 B) 1.5 C) 1.7 D) 1.9
    13·1 answer
  • Choose
    5·1 answer
  • .6(2k - 3) = 3(4k + 5)<br> Hellppp pleaseee
    10·1 answer
  • What is the value of the tangent of
    11·2 answers
  • Find an expression which represents the difference when (-3x + 5y) is subtracted
    6·1 answer
  • Evaluate x(6)2<br> When x = -4
    5·2 answers
  • Initially, 50 bacteria are placed in a Petri dish. It is observed that the bacteria triple in population every 8 hours.How can t
    6·2 answers
  • Lesson 6 Practice Problems
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!